Long, narrow rooms like this work best as two zones instead of one big one. I'd keep the hangout zone at the near end where the sofa already is and give the far end, by the half wall and the window, to the exercise bike or a game table.

Floor: over tile, a large low-pile rug is the easiest fix. Go big, 9x12 if the room allows, so the front legs of every seat sit on it; a small rug floating in the middle makes a long room feel longer. If you'd rather it feel like a real floor, carpet tiles or a bound carpet remnant cut to the room are inexpensive and warm up a basement fast. Either way, use a rug pad over the tile.

Paint: the lavender-gray reads cool next to the warm beige tile, which is part of why it feels unfinished. A warm light neutral on every wall (Benjamin Moore Edgecomb Gray or Sherwin-Williams Agreeable Gray) with a flat white ceiling will calm the whole room. The sound panels can stay; just arrange them in an even grid or recover them in one fabric so they read as art.

Furniture and layout: float the sofa off the long wall facing the wall where the TV goes, add two swivel chairs or a second small loveseat across from it, and use a big soft ottoman in the middle instead of a hard coffee table (kid-friendly, and great for feet). A console behind the sofa gives you lamps and storage. Lamps matter a lot down here; recessed cans alone always feel like an office. Big lidded baskets keep the play stuff so it still works for the kids.

Hope that gets you started. It's going to be a great family room!

Thank you so much!!!

I'd start with the floor and see how you feel about a darker flooring, then choose a paint color that works.

carpet tiles are a quick DIY

https://www.wayfair.com/VEVOR--24-W-x-24-L-Level-Cut-And-Loop-Polyester-Carpet-Tile-KCXFKDT2424YV0-L3593-K~FXNU4761.html?channel=GooglePLA&ireid=283206726&fdid=1817&PiID%5B%5D=99274453&refid=GX23521059292-FXNU4761_99274453&device=c&ptid=&network=x&targetid=&gad_source=1&gad_campaignid=23521063654&gbraid=0AAAAAD9ISC6EyuW9h-fRuenGZ8JDZHn_H&gclid=EAIaIQobChMIzqa1yp2_lwMVKjjUAR0cvDrJEAQYAiABEgJDY_D_BwE

Hoping those wall pieces are removable.

I would put the t v on the larger solid wall and make it a statement wall.

Leather sectional on the other wall.

Buy an area rug to ground the furniture. Go with performance. Lovely rug choices on this site and can be cut to fit your space. Set up your furniture first, so the rug is the correct size.

Far end, no tmuch different than what you have, upgrade the table and chairs...game table. Other end, what ever your family likes...pool table?

https://www.sisalrugs.com/performance-rugs

Yep. They are removable! Thank you so much for the advice! I love your ideas!!

the basement living space is an opportunity to do something fun/different just for the family to enjoy.

Doesn't need to follow the decorating style of the upstairs living spaces. How about a Team color theme? Decorating with team memorabelia, fun artifacts from travels, family photos... all the things you have but don't necessarily want them in your public spaces. Especially if you have children still at home.

Putting an area rug over the tile is an easy affordable quick way to "change" the flooring. Think about how many in your family, how do they prefer to lounge? Sectionals are not a favorite with me or mine. You end up at the mercy of the person shifting around next to you. Maybe you enjoy all piled together. Each family is different. When I chose furniture I made sure there was equally comfortable seating for each person. I ended up with a love seat and several chairs, rocker, swivel, foot stool, recliners. This is your space to relax not a space that needs to be magazine ready or filled with the latest trendy whatever's. I like to maximize sq. footage available for walking/playing. Floating a sofa on the narrow wall will square up the space, on the long wall could give you little clearance around furniture. Your ceilings look higher than an average basement, but painting the soffits and ceiling the same will add to the height. Never a bad thing! The banding affect is cutting off the room. LOVE your boardgame/crafting area with its storage etc.

Will suggest as one of your first steps to thoroughly think about all the functions that will be accommodated in your basement hangout space and go from there.