I believe Ubuntu 21.04 is "stable" as of today, but it has no Russian phonetic keyboard. All I can find in Hippo is the quaintly denominated "Russian (polyglot and reactionary)", which as far as I can see is identical to the standard Russian.
I hope the Russian phonetic keyboard is just around the corner. It has been on every long-term version of Ubuntu for at least 15 years. It is very useful for non-Russians and for people who type mostly on qwerty boards and only occasionally switch to Russian.
xkb-data
package as in 20.04 and 20.10, so nothing has changed. And multiple variants are available, including the one named Russian (phonetic). Possibly you are struggling with the GNOME settings GUI. If you have generated a Russian locale, the Russian keyboard layouts are shown in a sub menu which opens if you select Russian.