Hardware specs: https://boxmatrix.info/wiki/FRITZ!Box_4060#Overview
I'm wondering nobody asked, and this model isn't mentioned anywhere yet, still the previous 4040 seems officially supported. Any chance to have OpenWrt for it somewhen in the future? Doesn't have to be now, I'm just for evaluating since a new router is needed and I'll probably keep it for a long time.
Ps. If not, is there a recommendable router with support and similar or better specs?
Based on your link, it seems to be an ipq807x based device, for which support is still pending (but on a good way). However many modern ARM SOCs do have support for secure boot, which may throw a spanner into the works - in some cases this can be circumvented (by changing a u-bootenv variable via serial console), in some cases it may prevent any 3rd party firmware at all - in some cases the vendor left it disabled; there's no way to know this before trying (open device on the desk, serial console attached, trying to boot an initramfs image).
Chances for DECT support would be close to zero either way.
There are a few already supported (as in present in the pending development forks) ipq807x devices with similar features (no DECT) in that general price bracket (~200-220 EUR).
AVM devices usually have their bootloader, so it may be needed to replace it with U-boot