I just created a iOS Shortcut for this.
https://www.icloud.com/shortcuts/ea11ca3ef55948e8a2d34e9c9dda150c
So you can just tap the share button in any music app and then tap "Go to Songlink". (make sure you activate the Share Sheet option in the Shortcut)
I tested it for a few days and it works pretty much as expected. Sometimes it's a bit slow, but that's just the API of Songlink.

