Just yesterday I rented a tld for 2€/year and got it to update via my router's ddns feature using deSEC. Other similar services are available and I think that many domain rental services even offer their own ddns-like update routes.
All in all it wasn't that difficult, really. And imo an own tld is much nicer than having to rely on some subdomain of a ddns service.
So far (and yes, that is after less than one day) I definitely do recommend this.
It wasn't even the cheapest I could get. I rented a .de-domain from dogado.de, because I have made very good experiences with their customer services in the past.
1.111B class .xyz domain costs some 1 EUR per year. You're limited to <6-9 digits>.xyz format (e.g. 012345.xyz) but if that doesn't matter for your use case then this is the cheapest solution. You can get these via Porkbun, etc.
Maybe take a look at selfhost.de. The Website is completely in German but they have a free tier and their privacy policy also looks good.
I used the paid version for 10+ years and never had any problems.