Cox's Orange pippin

The waterlogging may have suffocated the roots and may have given fungi the chance to start rotting the roots. Some apple rootstocks are highly prone to crown rot when the soil is saturated. It can take as little as about eight hours of waterlogging to infect the roots in ideal conditions, but will take longer in cooler weather.
If you're lucky, there may not be any root rot fungi present in the pot.

The buds will be brown and leafless at this time of year, but will soon start to open and will be green underneath if you break them off.

Under the bark should be green, so your tree is still alive.

I suggest: get it out of the saturated soil immediately.

Within the next few days, neatly prune off any damaged twigs, or you will almost certainly get cankers entering (Cox's is very prone to disease).

The quicker you get it out of the waterlogged soil, the better the chance of survival. It still has a chance. Dwarf rootstocks often have some resistance to root rots (but not immune!).

Make sure that it is well cared for this year. However, don't feed too much nitrogen without potash because nitrogen can make the soil acidic, which would favour development of crown/root rot.
Unfortunately, it can take up to five years for crown and root rots to show themselves; you may have a ticking time bomb that will eventually kill your tree.

Thank you for such an informative answer.

Fingers crossed!