Fish version: 3.3.1-557-gb550b3885 (built from source)
OS version: Linux Mint 20.2 Cinnamon

When I define the following completion and write ./exe -first= option arguments are suggested:

complete --command exe --old-option first --arguments='1 2'

where exe - is a dummy empty program only to demonstrate the issue.

But man complete says:

Old style long options, like -Wall or -name. Old style long options can be more than one character long, are preceded by a single hyphen and may not be grouped together. Option arguments are specified in the following parameter (-ao null).

There is no notion about -old-option=value syntax support.