This year I inherited a pension from the UK, and to try to keep the paperwork simpler I also took a small UK pension of my own. Both have been paid as lump sums, and both had UK emergency tax withheld. I did the appropriate forms to get certification as a US resident for tax purposes. The UK tax authorities acknowledged this and sent a letter saying I will not owe UK tax for 2023/2024 and will be due a refund. All good.
The problem: the refund is unlikely to show up in 2023. The UK tax year is April-April, and they will probably do the refund after April 2024.
Based on the concept of constructive receipt of the income, you could probably defend claiming the net in 2023 and the refund in the year it shows up. But again, I would want to consult someone who actually knows the tax treaty and has an understanding of UK pension income.