Try latest git. Issues were found in SDK pre3 which is included in 2.5.0, so the SDK has been reverted to 2.2.1 after 2.5.0 release, ref #5784, see pinned issue.
Older core releases have other issues that have been fixed since, so reverting the core isn't enough either (you could be switching one reason that causes timeout for a different one that also causes timeout).

Latest git fails at SPIFFS.

Exception 3: LoadStoreError: Processor internal physical address or data error during load or store
PC: 0x40215f48
EXCVADDR: 0x402497b1

Decoding stack results
0x4020b148: spiffs_hal_read(unsigned int, unsigned int, unsigned char*) at esp8266\2.5.0\cores\esp8266\spiffs_hal.cpp line 45
0x4020b204: spiffs_hal_write(unsigned int, unsigned int, unsigned char*) at esp8266\2.5.0\cores\esp8266\spiffs_hal.cpp line 102
0x4020b340: spiffs_hal_erase(unsigned int, unsigned int) at esp8266\2.5.0\cores\esp8266\spiffs_hal.cpp line 168
0x4020ac60: SPIFFSImpl::open(char const*, fs::OpenMode, fs::AccessMode) at esp8266\2.5.0\cores\esp8266\spiffs_api.cpp line 30
0x40209db8: fs::FS::open(char const*, char const*) at esp8266\2.5.0\cores\esp8266\FS.cpp line 221
0x4020139d: Config::openConfigObject() at \esp8266_espino\Debug\Config\Config.cpp line 12
0x4020115c: BridgeApp::begin() at \esp8266_espino\Debug\BridgeApp.cpp line 16
0x40100124: millis() at esp8266\2.5.0\cores\esp8266\core_esp8266_wiring.cpp line 186
0x4020926e: __yield() at esp8266\2.5.0\cores\esp8266\core_esp8266_main.cpp line 100
0x402010a3: setup() at OOKBridge\OOKBridge/OOKBridge.ino line 25
0x402010a9: setup() at OOKBridge\OOKBridge/OOKBridge.ino line 26
0x40209234: loop_wrapper() at esp8266\2.5.0\cores\esp8266\core_esp8266_main.cpp line 122

I have of course error checking in my code. SPIFFS worked properly in 2.5.0.
There is nothing special in my SPIFFS code...

https://pastebin.com/yz1LLp1r

Your logs show 2.5.0. Either you're still using the release, or you installed git in a non-supported way.

I just checked latest git into 2.5.0 directory.

That's not a supported installation method. Please read the docs.

I've found, that this crash was caused by PROGMEM specifier on my filename variable.
Now testing, lwip2 is signifficantly more stable. Using lower memory variant, no disconnections for 53926 seconds, however test is still running :)

I've found that my router antenna was not original one.

Antenna has been connected using wrong SMA socket pair (female-to-female), which obviously didn't work. That was possible cause for all of my problems. Now (after adding an adapter) I have very stable and excellent signal (~ -30dBm).

My module is up for 41 hours now, without disconnection. However, I'd like to wait some more time, to definitely confirm that was caused by antenna.

Moved to another router firmware
(Openwrt), that allowed me to do some diag tests/scripts. There was a problem with LTE rsrp parameter, that sometimes cause timeouts, but doesn't restarts whole LTE session.

Changed network operator to another one. No problems, tcp connection is alive for 6 days now.

Conclusion: Never trust "conection time" status on router's configuration panel.

Please close this issue.