You cannot put skips in the prebreak, postbreak and nobreak texts. You can have a kern, though. It won't participate on space stretching or shrinking in the line.
Two methods, I'd prefer the first because it carries more semantic.
As you’ve found, the relevant pattern is u2s that overrides the pattern 1se, which would otherwise allow the hyphenation lau-se. The patterns for Finnish are mostly implementing straightforward orthographic rules, with only a few at the end trying to deal with compound words (u2s followed by 42 more). They can certainly be improved since they’re over ...
For the first part, a zero-width joiner (U+200D) as the hyphenchar:
For the second part, shrink and stretch (and therefore, hyphenate) is what TeX was designed to do. You can play with the fontdimens to see the boundary of the possible. A TikZ solution would probably be the way to go.
The stix2 fonts support neither OT2 nor T2A. Also using cp1251 is not the best way to type multilingual documents nowadays.
It's much better if you first convert your document to UTF-8 and then switch to T2A for Cyrillic text.
A good substitute for a Times-like font such as STIX2 is Tempora.
(I am generating an answer based on the comments with some additions).
My question is if it is typographically acceptable to force hyphenation in one-syllable words in rare circumstances?
It is wrong, but will it be tolerated by an English readership?
If not, what can be done to accomodate such situation?
Depends on the situation. ...
Building upon Cicada's answer, you can add character expansion with microtype; LuaLaTeX is needed.