I had a look on Wiki for this. The H2A appears to be an Australian degree classification which on the surface of it is our equivalent of a 2:1.
The grade boundaries look odd though with qualifying percentages in the 80's but some countries are like this.

A first class certainly isn't necessary for a PhD but both of the universities named above are ranked in the top 50 or 60 in the world (whatever the hell that actually means) so I imagine every man, woman, dog and small furry gerbil will be trying to get in there. A 2:1 equivalent, I would imagine, might be a problem due to competition in this case.

My advice to the original poster would be to expand your vision beyond the "top" universities in the world and you may find better fortune.

Don't worry, you won't get any brual responses on here unless you start making weird complaints about the hardship of having to carry a laptop to work each day :-D

Normally I would advise someone with mental health issues to get them sorted before undertaking a PhD because the PhD process can damage the strongest amongst us. I have still not recovered my sleep patterns properly 6 months after passing my viva and I got through the PhD without any major problems for example.
What is encouraging in your case is your statement about not wanting to let your mental issues rule your life. Make sure you remember that regularly as you go through the PhD process.

As for introversion and shyness? You will be in excellent company. Introverts apparently make up 50% of the population. We just don't shout about it. Academics are a weird collection of misfits. You will see many people who will make you feel like a party animal. I personally watched an academic panic and sharply dive into a shop when he spotted me on the high street to avoid just saying hello. Sadly for him but hilariously for me, it was an Ann Summers shop. I walked behind another person who did a u-turn when he saw me. He turned so quickly that he walked straight into the wall. Again, all to avoid saying hello. Hang on....maybe it's me that is the problem....anyway.......

In summary, I would say you are probably as good to go as you need to be but get those health issues seen to as much as you can before starting.

Good luck.

Use sci hub and put the DOI of the paper into the search engine.

I think ToL is being rather generous here. It may be poor wording but no reference is made to improving the quality of science whilst there are several mentions of the supposed quality of the journal. There is a tendency for scientists to assume that being published in a good journal somehow miraculously makes your science better than that published in lower ranked journals but this is patently not true. I am happy for the original poster to correct me here but it looks like an unhealthy obsession with impact factors and securing funding to me. Trying to get a famous scientist on board for the sole purpose of securing either high impact factors or funding is transparently manipulative and ethically suspect at best but it's up to individuals to decide how to pursue their own careers.

Marigold, it also seems clear that you are worrying about turning 50 and what material possesions you will have by then. You really need to stop thinking in those terms. Many of us are around your age. Not many 50 year olds go back to uni and get a PhD though. You will be joining an elite group of overachievers. You might be short on material crap in your life but you have made up for it with a whole series of very rare experiences and a more fulfilling life as a result. You also have the option of self employment when you finish. It would be a shame if you allow meaningless material desires to ruin what should be a brilliant few years for you.

Loads of people I knew from my first undergraduate degree 27 years ago are now Vice Presidents, Chairmen and Directors of massive companies and until a few months ago I was still at university (for the second time). It's easy to be jealous of their 6 and 7 figure annual salaries but virtually every one of them has sacrificed family and health to get to their position. A stream of broken marriages, bankruptcies and depression has been left in the wake of every single one of them. At one point I had to take an hour out of my studying to chat over the phone to a friend who was a successful director who was in total despair because he was 40 and had no kids. Just focus on what you personally want to achieve and don't worry about comparing yuor situation with anyone else. That would be my advice. Good luck.

You appear to be complaining a lot for someone who has just started their PhD.
You have a suitable laptop for your PhD. If you dont, upgrade, get the software you need and get on with it.
It's a shame the university might be changing how they operate the free laptop policy but this is the world of work for you. Funding changes and what was once promised suddenly doesn't materialise. Get used to it. You have 45 years or so of this in front of you.

You need to start maturing quickly because if this sort of trivial nonsense bothers you, the PhD will rip your soul to shreds before you are done.

You are overthinking this. Thank who you want to and omit those you want to omit.
I had some fun with this section. It started off all pompous and then I ended it in farce by thanking my dog for her support.

Anyone brainless enough to take up this offer of having anyone other than yourself write essays for you deserves everything they will get.
Quite apart from the extremely high likelihood of being caught because these scammers re-use phrases from other essays they have written for others, the scammers now have your bank details and your personal information and a golden opportunity to blackmail you for years to come with the very real prospect that they will reveal your cheating to your employer.
Like I said, if there are cheaters out there so stupid that they cannot appreciate the risks of this type of service then please feel free to get stuck in.

You are experiencing what happens to most people when they work from home without anyone to answer to. Learning how to self motivate is massive challenge in itself. Honestly I think things like external interaction (forums, emails, socialising) should be the reward AFTER you have worked through your to do list for the day. As I said in the other post you are engaging in classic work avoidance tactics.

enzyme, you could almost be describing me in your post.
The only thing you need to worry about right now is getting successful results.
Providing you can hold conversations in general as a functional adult, nothing else really matters in my opinion.
Dont do things you dont want to and dont feel pressured into it either.
Networking at PhD level is an overrated waste of time. You are only going to be talking to other PhD students in all likelihood. If you must network at all do it with people who are permanent academics or in a position to actually help your career. Be aware though that generally, those academics are not going to be interested in yet another PhD student reeking of desperation. Promiscuous socialising is a bad for you as promiscuous "romancing".
Honestly I wouldnt sweat this. You will know when it is time to start talking to other scientists because it will feel right.