According to a user on Reddit (and other Xbox Live subscribers), Xbox Games with Gold will not offer Xbox 360 games starting in October.
Reddit user u/Of_Silent_Earth shared the following message:
“Beginning October 1, 2022, the monthly games provided to Xbox Game Pass Ultimate and Xbox Live Gold members via Games with Gold will no longer include Xbox 360 titles. We have reached the limit of our ability to bring Xbox 360 games to the catalog; however, Games with Gold will continue to include exciting Xbox One titles and exclusive savings each month. This will not impact any Xbox 360 games that you downloaded before October 2022. Any Xbox 360 titles that you redeem via Games with Gold before that time are yours to keep on your Xbox account, regardless of whether you continue your subscription. Thank you for being a loyal member. Team Xbox.”
Microsoft later confirmed with GameSpot about this change. The statement was also shared earlier by @Wario64 on Twiiter:
Users have been receiving two Xbox 360 titles and two Xbox One titles every month, though there have been a few exceptions. On a few occasions, an original Xbox title has replaced an Xbox 360 title.
What remains to be known if what will Microsoft do next. The Xbox 360 games could be replaced with two more Xbox One titles for a total of 4. The number of games could also stay at the reduced number of two. It may still be too soon to add Xbox Series titles to Xbox Games with Gold.
[Sources]: u/Of_Silent_Earth (Reddit): Games With Gold will no longer include Xbox 360 games as of October – [Archive]. GameSpot: Xbox Games With Gold Will No Longer Offer Xbox 360 Titles From October – [Archive]. @Wario64 (Twitter): Starting in October, Xbox Games With Gold will no longer include Xbox 360 games (Microsoft has reached the limits to adding new X360 games to GWG) – [Archive].