The search engines for MySQL and SQLite treat "ＡＺ" (that's #xff21 and #xff3a) as "AZ" (cf. [[Halfwidth and fullwidth forms]]), PostgreSQL does not and thus fails testFullWidth().
One idea would be to TRANSLATE() them in ts2_page_text() and ts2_page_title() and use a similar technique in SearchPostgres::parseQuery(). If so, we need to describe in the release notes how to regenerate the tsvectors after an update or detect if ts2_page_text() or ts2_page_title() has changed and then regenerate them ourselves (I prefer the former).
Of course, another imaginable approach would be try to push this normalization into a text search configuration for to_tsvector(), but I don't know whether this is even possible.