Wikibase developers are willing to raise the minimum PHP version requirement of Wikibase extension to PHP 5.6, and, in other words, stop official support of EOL PHP 5.5 by this extension.
In general this change should not affect the production environment where Wikibase runs on WMF environment (a.k.a. Wikidata and Wikipedias) as there it runs on HHVM machines.
However, several of Wikibase scripts are run on snapshots hosts which are running PHP 5.5, so this change cannot happen until those hosts are updated to at least PHP 5.6, or (more likely) switched to run HHVM (T94277).
In other words resolving T86081 would most likely allow version bump for Wikibase. But T94277 seems to be the "smallest" blocker for this.
This ticket is a tracking ticket for all activities involving Wikibase and surroundings required to do the actual change of PHP requirement. More action items will be created as subtasks when "precondition" changes on WMF infrastructure have happened.