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The behavior of DateTime with Day.js (v1.8.17 on example page, same behaviour with current v1.11.3) seems to be strange.
This strange behavior can also be seen on the example page: https://datatables.net/extensions/datetime/examples/initialisation/dayjs

Steps to reproduce:

1. Open example page
2. Choose date 11. July 2022
3. The input field now says: "11/7/2022", which is correct (based on "format" option)
4. Click on input field
5. Selected date is now 6. November 2022

or

1. Open example page
2. The input field says "17/1/2020"
3. Click on input field
4. Selected date is 13. July 2022 (yesterday)

i18n doesn't work. Plugin is listening for i18n.dt event which is never called.
This is always reproduced with SearchBuilder. Picker is never translated to DataTable language