You file your 2025 tax return based on your legal marital status as of 12/31/2025, regardless of what it was for the other 364 days of the year.
If you divorce, each spouse is entitled to a $250K exclusion on their (single) tax return, regardless of whether you sell before or after the divorce is finalized.
You don't mention children. If there are one or more children under the age of 24 living at home, one or both spouses might be able to file as head of household after a divorce (or after a separation of at least 6 months) and HOH is a bit more favorable than single.
There are a number of downsides to filing as married filing separately. Assuming the divorce remains as friendly as it seems to be, and you don't have any significant disagreements or concerns, you can continue to file MFJ. The biggest legal issue is that when you file MFJ, you are taking joint and several responsibility for all the income, deductions and claims on the return—meaning that if there is a deficiency, fraud, or error, the IRS can come after either one of you, or both, or whoever is easiest to target, even after the divorce, and even if the error was by the other spouse. For that reason alone, you might want to finalize the divorce as soon as you can, or file MFS, even though the tax rates are higher with MFS, and many credits and deductions are limited or disallowed. (I suspect a divorce attorney would be horrified at the way you plan to remain entangled for 2+ more years. That's a long time for things to remain friendly.)
Note that under the rules for the home owner capital gain exclusion, if you were to move out now (for example), and get divorced in 2024 (for example), you would still qualify for your full $250K exclusion even if you sell in 2025 or 2026. As long as one of the exes lives in the house and meets the 2 year rule, the other ex is deemed to meet the rule as well, even if they moved out early due to separation or divorce.
I'm not clear on why you think you need to file MFJ for 2024 and 2025. Most of the time, the taxes owed by two unmarried people filing single will be very close to the taxes owed by the same two people filling as a married couple MFJ, and sometimes, the taxes for being married can be higher (the so-called "marriage penalty", although the effects of the marriage penalty have been reduced by some of the recent tax law changes.)
