Following the complaint to the DWG Ticket#2025022210000194 and the discussion above, I've reverted this in https://www.openstreetmap.org/changeset/162910810 .
To reiterate, I suspect that, based on the sources above _most_ OSM mappers (even ones like me who often map such infrastructure as part of the road) would map this as a separate cycleway.
If anyone would like to discuss this further I'd suggest doing so in a public forum such as https://community.openstreetmap.org (I can add a "lithuania" tag to any posts if so desired).  Discussing there would be better than a private location or a mailing list that's had one post in 6 months.
Best Regards,
Andy Townsend, on behalf of OSM's Data Working Group.
