Normally you shouldn't feel your tampon no matter what position you're in. Sounds like your tampon may not be in quite right. There's an awesome video https://www.ubykotex.com/en-us/periods/pads-and-tampons/using-a-tampon-for-the-first-time about tampon insertion that may help. Also, make sure you're using the right tampon absorbency for your size and flow so it doesn't slip.
There are a few reasons you may feel your tampon when you sit down, but I would guess that it has to do with the angle the tampon was inserted. Just like we all are built differently on the outside, we’re all different on the inside and a tampon may “fit” you a little differently. Try re-reading the manufacturer’s directions and perhaps try inserting it a different way and see if you end up with the same issue.
When it comes to tampons, there is no one correct answer. My daughter and I are built alike (on the outside) but have totally different choices when it comes to tampons and even pads. Good luck on your search, and I hope you find something soon that works for you!
It sounds like you are not inserting the tampon completely. I remember when I first starting using tampons, I was afraid to fully insert them and would often find they would get more uncomfortable when I sat down, especially if I attempted to use the tampons that didn’t have applicators.
Give the lighter absorbency tampons (with applicators) a try; you may have to change it more often (which is good practice anyways) and you’ll hopefully be a lot more comfortable!