The list is sorted by the date when the bounty was "awarded". Technically we don't have that date but the PostNotice gets deleted at the same time, so
- PostNotice.DeletionDate descending
should give you a close enough approximation of the order.
as proven by this SEDE query
select pn.postid [Post Link]
, pn.creationdate
, format(pn.deletiondate, 'yyyy-MM-dd HH:mm:ss:fffff') ["Awarded"]
from postnotices pn
where owneruserid = ##userid##
order by deletiondate desc
Compare the oddness:
For now this seems to be a stable order for your case. It might well be that the actual order by in the code turns out to be different and/or non-existing. The latter case is the prevalent implementation choice by SE developers. Not having an order by is more performant in which case the order of records is whatever SQL Server dreams up.
Yes, this order might differ with each run of the query. Note that in case of a tie (see the bounties on 2022-11-13) it is left to SQL Server in what order to return rows. In fact, SQL Server can return a different order for that specific case with each execution of the query. In the end that is an internal implementation detail that might/will change with each version of SQL Server.