Final answer:
A friendly stray cat that has chosen to spend time with you seeking attention is not unusual and indeed falls within typical feline behavior, much like a cat that seeks 'congrats' after catching flies. Identifying its owner involves checking for tags or a microchip. Taking in a stray cat alters household dynamics and is a significant commitment.
Step-by-step explanation:
It sounds like you have found yourself with a friendly feline visitor. Determining whose cat it is can be tricky if they do not have any identifying tags or microchips. Cats often choose to spend time with humans for comfort and affection. The behavior of the cat in your lap seeking attention and possibly congrats for their actions is similar to how one of my cats, Cotton, operates after catching flies, showing that cats often seek human interaction after achieving something they deem important.
If you're interested in keeping the cat and no owner can be found, remember that taking in a stray animal is a big responsibility and can change household rules, as it happened in one instance where a stray cat adopted by a family led to a change in the previously established 'No Pets' rule. Make sure to check for a microchip and attempt to find the owner before deciding to keep the cat.