Do we somehow support such technology as TMS (Tile Map Service)?
MicroStation plans to support the Web Map Tile Service (WMTS) in the CONNECT Edition Update 14. Is this what you are referring to?
https://www.opengeospatial.org/standards/wmts
Thank you Dan!
Do you have an idea when it will be realized?
Probably early in 2020, I can't say for sure.
You can upvote it here - https://communities.bentley.com/products/microstation/i/data_interoperability/support-wmts-web-map-tile-service
And also upvote fix for broken WMS 1.3 support but seems it could be postponed to U15 which would be really bad move and again cause more confusion - https://communities.bentley.com/products/microstation/i/data_interoperability/support-wms-1-3-0-version
I installed the MicroStation Up[date 14 beta release and see that the interface is there. I haven't used the tools so can't comment on it any more than that.