First off, the gateway bridge does no processing at all, only format translation between two different backhaul protocols. The transcribed radio packet itself, where both the fport and any payload are found is copied through entirely unaltered and not even interpreted - it’s just “I heard this on my antenna”. Processing only happens in the central servers. But even there, this kind of change is not made.
Packets sent on port 0 are network housekeeping traffic, likely part of a series of settings and confirmations between Chirpstack and your node’s LoRaWAN stack. They don’t contain application data, but they’re still important, having either an ack bit or a more meaningful response in the fOpts rather than they packet payload field. If there is network housekeeping traffic that needs to be sent up, and it cannot be attached to an ordinary application data packet (retaining that packet’s non-zero fport), then a typical node’s LoRaWAN stack will either send that instead of any requested application packet, or autonomously on its own, as a housekeeping-only packet on fport 0. A situation where the combination of housekeeping content and application payload would exceed the legal maximum (for that spreading factor, bandwidth, and location) is one where the stack would have to send the housekeeping traffic instead rather than as well. But it’s the node’s own LoRaWAN stack doing that - Chirpstack is NOT altering a message already transmitted. The one way that Chirpstack is involved is that the details of the conversation between network server and node would be different for different servers - Chirpstack and TTN aren’t going to be having exactly the same conversation in the same way, even if they need to send similar configuration down to the node.
If you want to understand exactly what is going on, you’ll need to post the full details of one of these packets, and also any downlinks preceding it.
Remember also that a given node can only be registered with one of Chirpstack or TTN at a time - if it were registered with both, completely chaos would ensue.