Tax on savings interest and the PSA (Scotland)

Cairnpapple

My question is about higher rate tax, pension contributions, and the personal savings allowance. Sorry I know that similar questions have been asked many times, but I can't get my head round it at all. 

I'm a Scottish higher rate taxpayer.  For round numbers,  let's say I have £51k income from employment + £2k savings interest in 24/25.

I make £5k of pension contributions using relief at source and claim higher rate tax relief for the difference between 20% and 42% on that £5k.

This is where I get completely lost.

I understand that the relevant tax threshold with respect to the personal savings allowance is the English higher rate threshold of £50270 not the Scottish higher rate threshold of £43662.

Is it the case that by claiming tax relief on my pension contribution, the basic rate band is extended by £5k (??) and the relevant threshold for the PSA increases to £55270 (???)

Does this then mean that my personal savings allowance is £1000 so I pay 0% tax on the first £1000 of savings interest and 20% tax on the remaining £1000 of savings interest?