I'm a sucker for replying to any sort of "how do I [career]" HN posts if they're relevant to my own experience, just can't help myself.
I also freelance exclusively, and opportunities come from word of mouth + the personal network that I've built over years of working with (or in) digital agencies. Full-timers jump from agency to agency at a fairly high clip and it's inevitable to run into people you've worked with before because they eventually need somebody and just think back to who they worked with in the past who they have fond memories of.
Generalism isn't a hindrance IMO because the job itself, like it or not, is a service job. You're not there to learn on the job, be part of the family, or find growth opportunities / upward career tracks inside of the organization -- you're there to help solve immediate problems, augment staff, and by God get things done. The more you know, the better! The way project resourcing works internally in these places is, the wider the skillset, the easier it is to slot you into a particular project that needs extra attention. The engagements are also pretty low risk for the agency since whatever you charge, they just inflate your rate to make sure they make money and pass it on to the client (which almost always gets paid), deliverables get delivered, the client is happy, and life marches on -- and if you're ineffective, they can just let you go with no notice, no offboarding, no extra costs, etc. For me personally, that's a win-win. For a lot of people, it's too much stress / risk / uncertainty, but different strokes for different folks!
Every now and then I'll get a gig or retainer that's more in line with "we're a small, thriving business, we need expertise, we have some budget, but we've also had bad experiences with small-to-medium tech shops. Help!" -- these are right in my wheelhouse because it's an easy retainer, quite low-risk for the client, and you can really make some meaningful impact on their bottom line as just one person.
You become "their guy", and the relationships can last for years and years and years. Again, this is a service job, and generalism REALLY helps on these types of engagements -- to be clear, you're not being paid to R&D a product or do academic research on cutting-edge algorithms -- you're just helping a client or business navigate the often-murky waters of technology to help them win. It might not sound "world-changing" in the context of big tech, but it can be quite satisfying work that really means something significant to real people just trying their best to make their thing go.
Anyways, to OP, good luck man! There's infinite opportunity out there if you've got the personality and the drive!