It's actually really straightforward.

• Start of input
• Followed by any number of groups of 4 characters from [A-Za-z0-9+/],
• Followed by one of the following:
  • [always matches]
  • Four characters where
    • The first and second match /[A-Za-z0-9+/]/
    • The third matches /[AEIMQUYcgkosw048]/
    • The fourth is a "="
  • Four characters where
    • The first matches /[A-Za-z0-9+/]/
    • The second matches /[AQgw]/
    • The third and fourth are both a "="
• Followed by the end of input

It's probably a bit simpler after the update I just did for you:

• Start of input
• Followed by any number of groups of 4 characters from [A-Za-z0-9+/],
• Followed by zero or one of the following:
  • Four characters where
    • The first and second match /[A-Za-z0-9+/]/
    • The third matches /[AEIMQUYcgkosw048]/
    • The fourth is a "="
  • Four characters where
    • The first matches /[A-Za-z0-9+/]/
    • The second matches /[AQgw]/
    • The third and fourth are both a "="
• Followed by the end of input

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