There are agreements on certain things like being an associate member of Horizon, as are other non-EU countries - the reason the Uk weren't participating was because they wouldn't implement the NI protocol properly. That has been resolved, at least for the time being. There are agreements on law co-operation and many other things.
The animosity between the UK and the EU is largely seen as from the UK side pumped up by the British press. The EU are mainly just getting on with other problems.
Someone coming along and saying they want to extensively rewrite the trade agreement will probably not go down very well.
The agreement is here (2530 pages of it):
https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:22021A0430(01). I wonder if Starmer has read it. It's due for review after five years which is really 2026, ratified by the UK and all 27 EU countries.
What is certain is that the many benefits available as being part of the EU/SM/CU are not available to a third country, which the UK has become.