Are they fully interchangeable, from a grammatical perspective?
fully? no lah. only in some occasions, “者” could be read as “也”
the quoted texts in the question, if one change “者” to “也”, or vice versa; the texts need to rewrite, slightly, imo
for particles usages in classical chinese, two books are helpful:
經傳釋詞 by 王引之
經詞衍釋 by 吳昌瑩
in 經傳釋詞 卷九, mentioned:
者・猶也也
roughly means: [the particle] “者” [could be read] as “也” [in some occasions]

in 經傳釋詞 卷四, mentioned:
也・所以窮上成文也
roughly means: [the particle] “也”, is for ending preceding [text] (窮上), [and then] becoming [following] text (成文)

have fun :)