I will say right from the get go no TV across from a large window . Media rooms are best when there is the minimum of natural light it will be easier to see when you post the plan how best to furnish.

You've likely got more problems than just seating. Windows and pocket doors are both no-no's in media rooms.

As @Patricia mentioned, that window will cause a lot of reflection on your screen. You'll also have problems with audio bounce and annoying rattles (unless all you watch are very quiet romance movies). The window coverings will need to be both visually blacking as well as very sound absorptive. The problem is that cloth can't prevent low frequencies from hitting them, that requires a solid surface. I have heard of people having solid sound absorptive panels in front of their windows but no idea how well that works and if it's worth the money.

Your pocket doors will need to be solid core with heavy rollers, tight guides on the bottom and solid locks to keep them from rattling. We have double pocket doors in ours and it took some effort to quiet them down.

What about Ikea's Friheten sofa. The 'chaise' can go on either side and it even converts to a bed (nice for those marathon sessions rewatching LotR =) It's 90.5" wide - so with one side up against the wall, you'd still have ~3' to walk by. Since there's no room for a side table, you could put a sofa/console table behind it - in addition to a coffee table in front. I've sat with 3 other adults on one (we were all good friends!)

Hard space to work with due to the small size, but anything can work.

I would have said use the 16' wall for the TV and just make 1 row of seating, but that pocket door wouldn't be good for flow. Because of that, I would hang a TV on the wall opposite the windows.

Hang decent blinds in the windows, then also hang big heavy blackout drapes above the window casing to really black it all out. There's blackout roman shades instead of blinds, can put temporary tint on the glass... I'm not worried about windows/glare.

Biggest thing for me is you don't want to be too close to the screen. You'd then have 10' width, to throw a full couch all the way back against the window, then either a love seat or modular chairs in front of them that would still be ~7-8' away from the screen (which is still very close). Or if it's kids and not adults, maybe beanbag chairs or something for front row?

Could even hang heavy curtains over the pocket doors if light leaks through and to help keep sound in. If floor is hard wood/tile, throw down fluffy area rug.

$3k is a very solid budget for decent seating and curtains/rug. Real question is how much your AV hardware will cost lol

What do you mean when you say media room? How is it going to be used? How many seats do you need or want?

Is this a movie room first and foremost or will it be the everyday after work and dinner relax place? Are your kids going to be playing XBox or whatever down there? Is it going to have a 5.1 sound system or 7.1 or just a sound bar? Whats the role or expectation for the space?

If this is going to be a relaxed room I'd go with a chaise like damiarainsuggested and add some bean bag chairs. If you have extra space in the back that looks empty add a foosball table or something like that to add an entertainment option and expand the rooms use.

If its a legit movie room I'd get a couple love seats and build a riser for them for tiered seating. In a movie room function takes precedence over form. Get it to sound right and get comfortable movie seats and enjoy the heck out of it and don't worry what it looks like.