The date format you're looking at is ISO 8601.
Strtotime() will convert it into an unix timestamp that is in UTC and you can save it to your database as a number. The number should be larger than 4 bytes so that you don't run in the Year 2038 problem. Everytime you read the value, you must convert it to the proper timezone of the user. This is the easy way. You'll never have to manually fix the dates in the database.
If you want to save it to database as a date, you probably want to still save the date as UTC and apply any transformations when you show the value. Convert it with gmdate() before saving:
echo gmdate( "Y-m-d H:i:s", strtotime("2021-07-09T14:09:47.529751-04:00") );
If you always show the value in one time zone, you can set the timezone in php.ini. This is not the best way though. It's best make it clear what timezone your program is using and explicitly set it in code.
When you want to show the value in other timezones, refer to this question or the manual of settimezone.