Thank you for your response. I'm glad you found the messages. :-)

Without any cycling infrastructure there is no need for tagging. No tagging implies cycling is allowed but no infrastructure.

It's also OK to use cycleway=no but it's not necessary. I would say such a tag might help on larger roads where one would hope for infrastructure but it's missing. On a small street like this, however, infrastructure would be very unusual.

https://wiki.openstreetmap.org/wiki/Key:cycleway
https://wiki.openstreetmap.org/wiki/Bicycle