Note regarding versions:
The regular version will have a file name ending in _rebuild_#.
Versions with a file name ending in _ungoogled disables embedded Google APIs in much the same way that "ungoogled-chromium" ( https://chromium.woolyss.com/ ) disables embedded Google APIs.
The "ungoogled" version is recommended for those that prefer tighter control over a Google-based browser basically giving special treatment to Google cookies and violating user preference settings.
A side effect to this approach (which also exists in "ungoogled-chromium") is that the Chrome Web Store is intentionally broken only in as far as the "Add to Chrome" button is concerned.
This is great for those that prefer to manually install extensions as opposed to obtaining from the Chrome Web Store.
A workaround to restore the "Add to" button (special thanks to @VistaLover for this solution) can be obtained from here -- https://github.com/NeverDecaf/chromium-web-store
Mileage may vary, for me this only added the "Add to" button but clicking it only downloaded the extensions .crx (which I personally prefer anyway) as opposed to 'adding to' 360Chrome.
I had similar results with official "ungoogled-chromium" on the official Chrome Web Store (restores "Add to" button but does not actually 'add to').
Special thanks to @Humming Owl for translated .png files.
Special thanks to @Dixel for discussions leading towards the "ungoogled" versions.
XP x86 SP2: v12, v13, and v13.5 work as-is in XP x86 SP2 but v11 requires special modifications - see this post by @we3fan
Download links for starting from scratch with a NEW PROFILE:
Regular:
https://www.dropbox.com/s/mes4wez1v34w9k4/360ChromePortable_11.0.2031_rebuild_8.zip?dl=1 (last updated: Jan 9, 2022)
https://www.dropbox.com/s/wol8va166au2p7j/360ChromePortable_12.0.1247_rebuild_12.zip?dl=1 (last updated: Jan 11, 2022)
https://www.dropbox.com/s/6lnst7yp0dt34s5/360ChromePortable_13.0.2206_rebuild_9.zip?dl=1 (last updated: Jan 11, 2022)
https://www.dropbox.com/s/8h4z346251wg7r8/360ChromePortable_13.5.1030_rebuild_6.zip?dl=1 (last updated: Jan 11, 2022)
Ungoogled:
https://www.dropbox.com/s/6z65t5yo08fr0ym/360ChromePortable_11.0.2031_rebuild_8_ungoogled.zip?dl=1 (last updated: Jan 9, 2022)
https://www.dropbox.com/s/j5zxk7aqv9ljjjc/360ChromePortable_12.0.1247_rebuild_12_ungoogled.zip?dl=1 (last updated: Jan 11, 2022)
https://www.dropbox.com/s/ld5dz2uwdowf1cz/360ChromePortable_13.0.2206_rebuild_9_ungoogled.zip?dl=1 (last updated: Jan 11, 2022)
https://www.dropbox.com/s/glulv6r8sce6xpy/360ChromePortable_13.5.1030_rebuild_6_ungoogled.zip?dl=1 (last updated: Jan 11, 2022)