Since you were filing jointly with K and otherwise married to him under common law, which is recognized in the statutes for Texas ,you are legally married to K until you get a divorce. It doesn't matter that you never registered the marriage with the county - you will now need to go through the process to adjudicate that marriage and dissolve it.
As already pointed out above, you can't file jointly with T because in 2022 you were still married, under Texas law, to K. A "common law marriage" isn't just a fancy term, but it is a legally binding marriage in states with common law statutes, such as Texas. What "common law marriage" (or informal marriage) means in Texas is that you've not registered with the county, but your marriage is just as legal as if you did. There are numerous ways you made it so, such as filing joint tax returns (something you can't undo.)
Technically, this means you weren't free to file your prior returns as single and should have filed them as Married Filing Separate. However, I'd be more concerned first with your current legal marital status.
The IRS doesn't verify or "recognize" your marital status when you file a tax return (there is no database of married people) - they simply process the return as you present it and challenges to your filing status would come up in an examination of your tax return (rare).
You definitely need a lawyer, not online reading on this topic, and you will need a formal divorce from K but to answer your tax question- your correct filing status choices for 2022 are either Married Filing Separately (from husband K) or Married Filing jointly (with husband K). (Unless you have a dependent and qualify to file as Head of Household.)
As an aside, and it's not your problem really, but K's current marriage isn't legal because he never legally ended his marriage to you. Texas wouldn't tell him to stop - the law doesn't work that way (in part because marriage, divorce, and death records don't "talk" to each other so they have no way of knowing if he's married or not when he files his marriage application in most cases). They take his word that he's legally free for marriage. The way the law does work, though, makes his current marriage null and void and makes you his legal wife until you divorce. (And while Texas law does allow you to pretty much act like the marriage never happened, that would then mean you filed a number of years of fraudulent tax returns. I think the divorce is the better deal there.)
