IMEI is the global identifier of the phone (modem). It needs to be transmitted for a phone to work in a normal phone network. Can’t be helped. There are of course special networks etc. but let’s not go there now.
IMEI cloning, is not what you learn from movies, it does not clone your phone’s content. It creates a duplicate IMEI to the network, a copy of your address that receives the same connection. For some reason the network standards don’t seem to care if there is more than one and send everything duplicate [edit add: old networks don’t, newer have tried to make it more difficult]. That is why SMS and voice over phone can be intercepted and heard (often referred to as IMSI catching, type of man in the middle eavesdropping), as they use the phone network. But you can’t control the original phone with IMEI alone. If you are using a messaging app that uses data (as the network connection is a separate layer) on the other hand… I’m not sure, but I doubt that data can be intercepted, and at least with E2EE it can’t be read (because the MITM would need the encryption keys too).
There are some (droid) apps that claim to identify IMSI-catchers but those have limits as they are not able to access firmware (… which I guess could work better in L5). Changing the modem is a countermeasure option on L5, which is better than other phones, but not a very convenient or cheap one (compared to likes of this phone, at least). In theory, it seems IMEI randomization is possible to do, but is it possible on the L5’s modems and what would the network provider (or local law) think…?
Anyway, if you have something very private to talk, you don’t do it over the phone and/or in plain english - or even in english.
[edit to add: there was another thread about hijacking SIMs to attack 2FA and I’d see that this could also be used for that - probably more damaging than eavesdropping - as open SMS 2FA is not really secure (although a bit better than not)]