L2 bridge of WiFi access point to anything else (like wired Ethernet, for example) "just works".

On the other hand, L2 bridge of WiFi station to anything else (including STA<->AP bridge for a repeater operation) is quite messy: it needs special "4addr mode" packets which are only sent in "WDS" mode, which should be enabled on corresponding uplink AP. And WDS is universally disabled out-of-the box. Many cheaper routers don't have WDS at all. Plus, there are different incompatible flavours of WDS. Finally, there is question of WDS/4addr mode support on ESP8266 itself - in theory, there is some support in SDK, but I haven't seen any working application code doing it.

Some in-depth discussion of WDS with diagrams:

https://wiki.openwrt.org/doc/howto/clientmode

https://www.dd-wrt.com/wiki/index.php/WDS#Note_about_WDS_and...