Usually with polycoms depending on the cloud pbx *0 then the ext will intercom. Which is different from paging . But to do intercom you need to change some settings/config. You don’t want intercom to barge in while someone is on a call putting them on hold so the intercom caller gets priority. You might also want there to be an audible ring before it connects the intercom.
VoIP
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because I cannot promote any solution by name for this issue (Terms) I would suggest the 250.00 SIP PBX, as a local fix it. it has the station, trunk, paging and Hunt groups all built in with no additional licensing cost. You can still run the cloud accounts direct to the ISP, and the second lines can be accounts on the local SIP PBX.
Direct IP Dialing
https://docs.poly.com/bundle/rpcs-ag-8-10/page/t4445600.html
I will check this out. Thank you!
The description your user gave was one phone calling another phone, but then you described it as "intercom/walkie-talkie/phone to phone on the LAN" which isn't the same thing, so I'm a little confused. If they just want to be able to make calls from phone to phone, you can either use direct IP calling or get a cheap PBX, the intercom/walkie-talkie would be called paging, which is something else entirely and not usually done through phones but through paging interfaces.