This widely varies but all AMR units have ESChat PTT on the devices they carry, some business units adopt onto the local dispatch channels whether that be trunked or conventional, analog or digital, however they're also known to have their own completely separate equipment used, sometimes patched to their served jurisdictional dispatch channel/talkgroup, so I wouldn't be surprised if you only hear an initial request for EMS on the DMR medical talkgroup and all of their other traffic is over ESChat or their own equipment. You may try close call or check for frequencies in the area licensed by them. If they have a medical tent/aid station setup you may be able to walk by there and glance at what they're carrying.
For LE, it's likely the police operate on TXWARN while they have a command post or a designated Officer/Sgt with another radio to monitor the DMR police talkgroup for any LE requests, none of this would be heard by the Officers in the field. Just like I suspect in the case of AMR, an initial law enforcement request would come over DMR, command post officer would write down the information and then relay it over their TXWARN talkgroup. Same thing with this, if you see an officer check what radio they're carrying and that'll tell you.