There is no real linguistic definition of a “pronoun”.
Grammatically, however, words that are often called “pronouns” in Japanese behave in an identical distribution to any other normal noun.
But, there are a couple of words in Japanese, specifically those whose nominal form ends on /-re/, such as /sore/, /ware/, /kare/, which distribute slightly differently from normal nouns, in no small part that the actual stem of /sore/ is /so-/, not /sore-/, and that /-re/ is a suffix used in nominal use, the adnominal form is thus /sono/, not /soreno/, and with /ware/, it is even typically the irregular, archaic /waga/, not /wareno/. In older forms of Japanese normal nouns indeed took /-no/ to form the adnominal form, and these took /-ga/, but this distinction has largely been lost and /-ga/ has been repurposed to form the nominative case, which was unmarked in older Japanese.
Are these pronouns? they are certainly grammatically different from other nouns, which say /watasi/ is not, but there is no linguistic definition of a “pronoun”, and you will find that most linguistic terms are defined on an ad hoc basis from literature to literature with little consistency to them and are often in want of an actual definition.
It should be noted that in English too, noun phrases are often used with semantic pronoun-like function and distribution such as “your honor” or “his highness”. And in terms of “substitution” English too can substitute many phrases such as “the lad” or “said actor” for another phrase to avoid repetition. — are these pronouns?
One thing one can say is that the class called “pronouns” in English in the traditional sense is a clearly defined, unambiguous exhaustive group, just as the class of Japanese stems that take /-re/ to form a nominal are, but what other “nominal phrases” are and aren't “pseudo pronouns” in Japanese is not so clear, as it is in English.