No, an IMEI does not give file access on smartphones
I'm not knowledgeable about older phones and the weird apps they built into them but smartphones have no such capability unless the carrier has built some horrible spyware into your phone. Most of these "track a cell phone with just the IMEI online" things are complete garbage and mostly fake. The IMEI is just an identifier for the phone so that carriers can know which physical device it is talking to.
Knowing an IMEI can have a different impact if you have access to the carrier database or not. Without the database you can maybe tell what model phone/ generation it is however these databases often have multiple matches since the data isn't well coordinated. IMEI does not give a specific purchase date or carrier but these databases make assumptions because generally IMEIs are assigned in order. Warranty information is guessed based on this information. All information here is static-ish. They are not polling your phone however sometimes the information could change if they get a new data set.
Things get a bit fuzzier when you are the carrier because they have a lot more information and communicate directly with your device, unlike any of these IMEI sites. The carrier is in a very privileged position because they can control SIM apps which silently can run on the microprocessor on your sim card. Here's a very very cool DEFCON talk about this. With this and their ability track you they have a huge amount of information about your device itself however they still don't have access to your data unless they are actively exploiting and attack your device. Any information the carrier receives is reported by the OS. The carrier isn't accessing the phone and reading the version property but instead asking the device what version it is. All of this, of course, assumes that the carrier hasn't added some nasty tracking software however AOSP/iOS devices should be entirely clean.