Working through all of Peter Smith’s suggested books from the original post should give one a solid understanding of much of what’s been going on in field up until fairly recently. Every recommended book in Smith’s list from the original post up to and including Shapiro’s The Oxford Handbook of Philosophy of Mathematics and Logic also appears in Avigad’s suggested readings from your link, several under the section on contemporary developments. I think it’s a plus that Smiths list is more focused. Smith’s list also contains more recent works that do not appear in Avigad’s list.