How to make the best usage of my current time in an unmotivating environment?

Sorry to hear about your situation - It definitely doesn't seem fun. Unfortunately, there are a lot of bad jobs, even in the cutting-edge tech industry, so this career trap happens to a lot of people.

I have 2 broad pieces of advice here:

1. Getting into the work
2. Disconnecting from work

Getting Into The Work

• This means trying to make the most of your current position, upskilling and growing within it. I would give this a chance for a couple months at least.
• First, unless you aren't making enough to live decently, I would treat compensation as a secondary goal. Of course, money is important, but having it top of mind constantly is very draining, especially when you're comparing yourself to the rest of the market (there will always be some ultra-talented FAANG engineers making 2x what you are). My mentality across my entire career has been to grow as much as I can and that my compensation will eventually "catch up" to my skill (which it did). For most people, compensation will be a lagging indicator, and I talk more about how to view compensation as a career goal here.
• Manager with too many reports is very common and is something I've faced several times myself. The main way to mitigate that is to find a mentor on top of your manager, usually an IC more senior than you. Here's our advice on how to do that.
• To help with your confidence and leadership skills, I recommend this discussion on how to be more assertive in the workplace.

Disconnecting From Work

• What this means is doing the bare minimum to comfortably meet expectations, which should generally leave you with good work-life balance and several extra hours after work.
• There's nothing wrong with having a career goal that isn't growth related. There's a lot of pressure to be constantly increasing your TC, level, and prestige of the company names on your resume, but it's important to ignore all of that and focus on what's best for you. In your scenario, it could make a lot of sense to just meet expectations at your current job (staying at your current level/TC) until the job market warms back up again, doing fun stuff on the side in the meantime.
• One option for that "fun stuff" is side projects. This is a way to build up skills for your career without overworking yourself. I was in a similar situation to you back at PayPal. I was underpaid, promotion was slow/political, and I wasn't learning/motivated. To deal with this, I spent 4+ hours a day working on side projects, which eventually gave me the skills I needed to switch jobs and land a 50% TC increase. Here's more of my in-depth thoughts on using side projects to level up.
• The other option is just to pick up hobbies and spend more time with friends and family. This more "wholesome" energy is something I see a lot of people in tech fail to tap into enough - There's more to life than just working and doing this just helps keep you sane in general.

4+ hours a day on side projects! How much of that was at work versus outside of it?

In my 2nd team at PayPal, I was able to get the work done in 2-4 hours most days. This team had a lot of "WFH" even though this was pre-covid (teammates mostly didn't do anything during their WFH days). During my WFH days (2-3 days a week), I finished up my work by 2PM and just worked on side projects for 4+ hours after that.

When I went into the office, I would leave early at like 4PM to hang out with 2 friends (they both lived near San Jose campus) to grind through side projects together. They also didn't like eBay/PayPal, so we all left within 1.5 years.