Just ran into this one after installing the latest/greatest for today; SSMS 21.1.3 & VS22 17.14.3. Same deal- Import Data not actively showing up (ie greyed out) within SSMS.
And as @feganmeister mentioned, one can still use the utility. Just set up a shortcut. There are two versions; 32/64 bit. I brought mine up from C:\Program Files\Microsoft SQL Server\160\DTS\Binn\DTSWizard.exe.
I did, in fact, try uninstalling VS22 SSDT and reinstalling...same result; no active Import Data option under Tasks. I just reinstalled SSMS. Same result- no active import data option.
I realise this is an older (6 years ago) issue, however, it might be still going on via the new installers. Cheers!