I guess you're right on that, I hadn't read the website in a while and I only skimmed it when I did.
"A trademark application must specify the proper "basis" for filing, most likely either a current use of the mark in commerce or an intent to use the mark in commerce in the future." (from:https://www.uspto.gov/trademarks-getting-started/trademark-basics)
I guess I'd just be wary of jumping into register too early, before you have proof of the 'intent to use in the future', because if you apply and they reject the application, you've lost money on that. Idk where you are in your process, but just keep that in mind.
The first video, "Basic Facts 01" is a good video that goes over the basics. He discusses trademark selection challenges & how to search the database to ensure your mark isn't already registered at around the 15 min mark. He also discusses what to look for and ask when hiring an attorney to file a trademark application for you toward the end, around 30 mins in, and I'd check that out if you're really interested to make sure you've covered your bases with your lawyer friend who's offered to do this.
However, I still wouldn't really worry about it until you're really promoting your music and getting out there (like on radio/larger venues, at least regional tours, or when you start needing sponsors and stuff). The likelihood of someone 'stealing' your name is very low right now, and will probably remain so for a while. I'd make a goal of 'play x amount of gigs' or 'get over x number of facebook/social media followers' or 'sell x number of tshirts/merch' or 'sell out a venue of x number of people' or 'play on the radio' or 'get x number of streams' before I would put money toward reserving a trademark.
Now for the domain:
It sounds like the domain you want is already registered by a reseller or squatter. I would not recommend paying that amount for a domain at this time.. maybe if your band hits it big, but even then you could use "stonetssband.com", "stonetssmusic.com", "stonetss.band", or any number of variations that are available. Same goes for your social tags, which it sounds like you've done. Your fans will figure it out.. they're probably using links to find you anyway. When you're ready for it, you'll be able to sort out the SEO later.
To check if a name is available, go to your computer terminal/console and type "whois mydomain.tld" (see: here). You want the query to return "no match for domain" (see: here), which means it's available to register. If it returns with a bunch of registration info, check the status. If it says "Active", keep searching & trying variations in the terminal until you get one that is available. If you see something like 'pendingdelete' or 'redemptionperiod', that means the domain may expire from it's current registration and become available, and you may want to research dropcatching the name to get it... but that's a whole 'nother post (I had to do this.. it was a pain and a half!). If it's simply marked 'ok' or 'transferprohibited', that means it's already registered by someone else (or a squatter/reseller) and is in good standing, so they probably won't just let it expire, and you probably won't get a chance to scoop it up later, so I'd move on. It's not that important to have the perfect domain... most people aren't looking for you on a website anyway, and if they are, they're finding you via a link.
I get that it's hard to find stuff to do while waiting on recording, especially during this time when gigs are so limited. If you want to be ready to hit the ground running, I think the better use of your time is to start learning about SEO and how to promote yourself, and make a bandcamp page for free so your stuff can go straight on there when it's ready. Also, look into distribution stuff (like how distrokid works & how to get your stuff on streaming platforms/where/how you want to promote your music). There's tons of resources on here for that. Find fb/social media groups for musicians in your area or genre and start networking that way if you can't go out and see people/play. They'll be your first resource for promoting your album when it's finished.
Maybe work on some visual art to use for album covers, t-shirts/merch, or social/website designs, or work on a logo if you need a break from practicing or producing on your own (or reach out to other artists who could create this with you if you don't want to create it yourself.) When I get burned out playing, it's helpful to look into ways to express my band's identity through other mediums, so I stay semi-productive, and maybe learn more about what I want my band to be and stand for.
And there's nothing wrong with just practicing like a maniac and working up your skills. Maybe try a new style or genre that you're not already great with, which could lead to new songs. I took a free Berkley online class through Coursera last winter, which really helped jumpstart my lyric writing, that might be a good change of pace too if you're burnt out playing and feel like you're just waiting around. It's always good to have extra songs lying around for future albums.
Hope that helps!