Many older extenders/repeaters did allow you to set them up as a wireless client, which would convert the wifi into a single ethernet port. Unless this also toggled on a DHCP server (in which case the wifi radio would be treated as the WAN port), this would only work for one device at a time even if an ethernet switch were attached to the single port, generally only providing internet for the first attached device to be powered on. With a DHCP server this would put it into double-NAT and usually only work with IPv4 and not IPv6 for all attached devices.
Given all the ways it could be set up wrong to cause support issues and the no-IPv6 limitation in an age when over 40% of internet traffic is now IPv6, it is no surprise that modern extenders typically omit this capability. Your EAX15 can only be set to extender/repeater mode or wireless access point mode (which is all its ethernet port is for) and not a client.
If you have an old wireless router laying around, FreshTomato's Wireless Client Mode and DD-WRT's Station Mode will do this double-NAT thing for you and even give you 4-5 ethernet ports since routers include a switch. DD-WRT also offers Station Bridge and Repeater Bridge modes where both routers share the same MAC address on the same subnet, but those use WDS for IPv6 capability which can only be implemented as an ugly VLAN hack on Broadcom devices which turns out to be pretty unstable. Likewise, the FreshTomato wiki suggests WDS has not been recommended since 2022. I don't know if you'd have better luck with an Atheros/Qualcomm or MediaTek powered device but while their drivers probably don't require this workaround, I did attempt this on an old ath9k router running OpenWRT and it would also only work in double-NAT.