Green card holder physically present in US but employed, paid and taxed in UK

US/UK advice needed as I become more and more aware of how complicated my situation is:

I am a US Greencard holder through my wife as of July 2020. In 2020 I filed as a dual tax resident on my own through turbo tax that seemed fairly straightforward. For the 2021 tax year, I have spent over 183 days in the US while employed by a UK company, paid into a UK bank account, and have UK tax withholdings on my salary (PAYE). If anyone can point me to an expert in this area that would be fantastic!

 

My key questions/concerns are:

Can I claim a credit on my UK-paid taxes through the US UK dual tax treaty?

If not can I have to claw this PAYE tax back from the UK HMRC and pay the IRS?

Should my employer have been withholding tax for the IRS or doing any other sort of reporting?

As I am physically present in the US could my employer owe tax?

Anything else anyone has come across in a similar situation?

Any and all help is appreciated. Thanks