I found an actual adjustable hydraulic shock for the Birdy from Multi-S. I suspected someone must make a real shock for this bike, but wow this is expensive.
https://www.ebay.com/itm/Birdy-100-285-Adjustable-Hydraulic-front-suspension-shock-Multi-S-G5-PLUS/192340072672?hash=item2cc85c98e0:g:mmAAAOSwTmtZ6swB