You had 60 days to put the equivalent amount of money into the Roth, that would be considered an "indirect rollover", not a contribution, and would have been perfectly legitimate even if the money spent some of those 60 days in your checking account. Unfortunately, the 60 day window has passed. If you can reasonably claim that one of these circumstances occurred which delayed you from making the the correct rollover on time, you can claim a waiver of the 60 day rule and do a late indirect rollover.
1. An error by the distributing or recipient financial institution;
2. A misplaced distribution check that was never cashed;
3. A distribution deposited and remaining in an account that the taxpayer mistakenly thought was an eligible retirement plan;
4. Severe damage to the taxpayer’s principal residence;
5. Death of a member of the taxpayer’s family;
6. Serious illness of the taxpayer or a member of the taxpayer’s family;
7. Incarceration of the taxpayer;
8. Restrictions imposed by a foreign country;
9. A postal error;
10. A delay in obtaining information from the distributing plan or IRA that was required by the recipient plan or IRA, despite the taxpayer’s reasonable efforts to obtain it; or
11. A return to the taxpayer of the proceeds of a federal tax levy on a plan or IRA.
You might have #5 or #6 and not told us, but from your story, the others don't seem to apply. You would have to decide if you want to argue #3, but I think you probably knew right away that it went into the wrong account, and you took too long to fix it.
In that case, you now have money in your checking account and that counts as a withdrawal and you have to pay tax on it. You can do anything you want with the rest of the money (such as invest it).
You can't make any contribution to a Roth IRA unless you have compensation from working (wages or self-employment profits) and even then, the maximum contribution would be $8000.
However, you might be under a misconception about the tax. If your intention was to take pre-tax money in a 401(a) and roll it over to a Roth IRA, that would be a conversion, and would be fully taxable. You would pay the same tax that you have to pay now. The difference is that your future gains would be tax-free in the Roth. Now, if you invest the money in stocks or bonds, you won't have to pay tax again when you withdraw the principle, but you will have to pay tax on any interest or capital gains. But, depending on your marital status and other income, your capital gains tax might be very low or even zero as long as you hold your assets at least one year.
You should probably see a financial planner to help you work out what to do next.
You can ignore the issue of any RMD, that would only apply if you were able to complete the rollover, which you can't. Your complete withdrawal includes your RMD for 2025 as a small part of it.
