I see you didn’t spend a week sick in bed with no fresh reading material except for a copy of the TeXbook :) Exercises 9.4 and 9.5 from the chunk of exercises on diacritics there mention ‹Akademii͡a› for ‹Академия› (usually ‹-ija› or ‹-iya›) and ‹I͡urʼev› for ‹Юрьев› (usually ‹Ju-› or ‹Yu-›), which I remember (sans the numbers of course) exactly because I had never before seen that romanization[1] and thought it weird. But apparently the Library of Congress does use it, and if you can get hold of official English translations/selections of Soviet physics or mathematics journals from the 70s and 80s you’ll see the authors’ names spelt according to it as well.
Note that in modern times, you’re supposed to use the tie to spell affricates and such in IPA as well, like in ‹t͡ʃ› and ‹d͡ʒ› and, yes, ‹t͡s›, even though nobody does as far as I’ve seen.
Alas, I read the TeXbook originally in 1986 and while I've dipped into it a lot since then, I've not re-read it in its entirety since that first read. I'm the one responsible for adding a section about the ALA-LC romanization in Tie (typography) on Wikipedia.
Note that in modern times, you’re supposed to use the tie to spell affricates and such in IPA as well, like in ‹t͡ʃ› and ‹d͡ʒ› and, yes, ‹t͡s›, even though nobody does as far as I’ve seen.
[1] https://en.wikipedia.org/wiki/ALA-LC_romanization_for_Russia...