For a successful installation of TinyCP on my home server I had to go back to Ubuntu 18.04. Otherwise, Tiny bleats when installing. But what prevents me from upgrading the OS if it's already running well? Nothing, it's my own server. If it doesn't work, I'll start over again.
But it went all right! Yippiayay!!!
It was actually quite simple: in /etc/apt/sources.list, replace all entries of 'bionic' with 'disco', the codename of the new release. Then apt update && apt dist-upgrade && apt upgrade && apt autoremove && reboot. And then we landed in the disco version of Ubuntu, which included a running version of TinyCP and running versions of all TinyCP installed servers, such as Apache2, Postfix, and Dovecot. And, oh yes, everything now runs under php 7.3 instead of 7.2.
Was a successful day!
And while I was at it: TinyCP installs all user data, including email and websites, in the /var folder. But that was just a default folder under the root of Ubuntu. That started to get pretty big... Back in the day, when I was still doing everything by hand, I put it in /home, which was a folder on one of my data volumes (with a few TB of space, and in a file system that is more favorable for smaller files, viz. Reiserfs). I have now done the same with /var. Something like that is a bit tricky, but it worked out nicely. First renamed /var to something else and then immediately made a symbolic link from that something else to /var. Then quietly copied the renamed /var to the new location and modified /etc/fstab, so that henceforth /var will be bound to a folder on the data volume. Then a reboot, and sure enough, it works!
That means that if the SSD on which Ubuntu is installed should fail, I can still access my data, because it runs on 4 RAID-10 HDs of gross(!) 6 TB each.