This. You’re bound up and your muscle mechanics have regressed as a result. Your glutes, hams, psoas, abs, low back, and piriformis have all been tightened (and weakened) from sitting so much. Upper back is probably compromised too with shoulders rounding forward over a keyboard and steering wheel. After you squat, these same muscles get even tighter as a result - which is what drives your pain the next day. I would bet that your left side is your non-dominant side or weaker side? Which is why you’re feeling it there more than elsewhere. All the same things for me.
The fix - as others are saying - mobility, but also strengthening the weaknesses as well as try to limit the time you’re sitting as much as you can. From personal experience I would look at Matt Wenning’s warm ups or Dave Tate’s warm up in addition to some mobility work. The gist of Wenning and Tate’s warmups involve picking 3-4 areas you suck at - in this case hamstrings, abs, glutes, etc and focus on them to add additional volume to build them back up prior to your workout. Wenning prescribes 4 x 25 reps in a circuit fashion. The high reps are meant to keep the weight low. The biggest one for me on the Dave Tate side is the hanging leg raise (toes to bar) to open the hips and low back, and strengthen the abs. The first set will show you just how tight and weak sitting has made you. I would also suggest moving to a box squat with a wider stance to hit your hams and glutes by sitting back. This will also point out how much weaker those areas have become. You will immediately feel the ham and glute struggle when you stand up off the box.
On the form side from your videos, I see the above reflected in your reps. In the second video, look at your setup. Notice how uneven your hands are? Your left is in tighter than your right. May be just a set up piece, but could reflect upper back tightness and imbalance too. When you descend, your heels start to raise because you’re tracking forward. In the third video, this is confirmed by your bar path and your chest falling forward. Put a pencil vertically from the bar to the floor against your video at the top of your rep. You want the bar to track pretty close to up and down, keeping the bar over the center of your foot. You’ll notice that you track way forward. It looks like your chest drops (elbows are pointed way back) pulling you forward - bar path (vid #3) and heels raising (vid #2). Abs are not holding you up. Also, your head is not neutral. You’re looking down.
The fix - Mobility (Agile 8), hamstring/glutes, abs/low back, and probably some upper back volume added as part of your warmups consistently (even on non squat days) to build that strength back. Then go to a box squat with a wider stance to target and build up the hams and glutes even more. Then it’s technique - head position, tight core, even grip on bar, etc. It takes time to build it back and I was surprised with how light in weight I had to regress to, but it’s worth it. Stay consistent and it should be a big change for you!