Signal has a built in 'export' function that produces a plaintext file with chat logs. However that might defeat the point of end-to-end encrypted messages.
Another approach is to use Signal's "Linked Devices" capability. Designate a central "device" (server) for FOIA purposes, and mandate all relevant public servants/elected officials using Signal add that as a linked device.
Then there's no need to retrieve a device and dump its message store, which obviously depends on the device being in a functional state. Instead there's a one-time setup when Signal is first installed.