Just a few points to make.
With vaccines, the main issue is the documentation around the vaccination. There is currently no global standard. Fake documents have been used. Even the card you are given in the UK showing your vaccination status is, i am told, not valid for global travel - you have to take your card to a GP and get another document. At the airport in the UK, the average border force person can barely read, let alone decide what is and what isn't a valid vaccination document!
next, the PLF form. I wouldn't say it was easy, especially when you do not know the questions. Took me about one hour to do, as i had to keep saving the form and going to check information requested (i was isolating away from 'home'. which complicated it a bit). It is sent to you as a electronic document via email, you could print it, but if you can access it on your phone should be OK. I gave my Thai mobile number although i knew it wouldn't work in the UK. Even after i returned and got a new SIM, still an issue as where i was isolating there was usually no reception, it is a dead zone. Fortunately i also gave the house phone number and they contacted me on that a few days after i arrived. Not sure how many times they tried to call because it was hot and i was in the garden....
Checking - At Bangkok they asked for my 72 hour Covid test and the PLF, but didn't really scrutinise it. At Amsterdam, we were sent to a special document check location and they were examined in some detail. They put a sticker on your passport without which you could be denied boarding. At Heathrow - no checks at all! I received one telephone call and a home visit from a real person at about day 6.