One way they get away with using relatively few tubes is that most of the Boolean logic is done with semiconductor (germanium) diodes, using tubes to amplify the results.
https://lampes-et-tubes.info/cd/cd053.php?l=e
Or the complicated and impressive storage tubes, that would fit 16 kbits of RAM in a single CRT:
https://lampes-et-tubes.info/sc/sc022.php?l=e
By the way, this website is one of my favorite finds on the Internet and very long-running.
For a while, you could get things like bucket-brigade CCDs for analog signals (used for reverbs and suchlike). They're still made in small quantities, I think, by boutique operations like Xvive.
Also, there was the ISD ChipCorder, which was actual analog Flash. (Current devices are digital, but the old ones were for a while sold as "MLS ChipCorder" by Nuvoton.)