You should be able to reach local network running in bridge mode, here's a test from my local server pinging the laptop, executed in a docker container

root@dalek:/# ping -c1  192.168.8.167  
PING 192.168.8.167 (192.168.8.167): 56 data bytes  
64 bytes from 192.168.8.167: seq=0 ttl=64 time=0.440 ms  
\--- 192.168.8.167 ping statistics
***
 
1 packets transmitted, 1 packets received, 0% packet loss  
round-trip min/avg/max = 0.440/0.440/0.440 ms  
root@dalek:/# ip route get 192.168.8.167  
192.168.8.167 dev eno1  src 192.168.8.136

Host mode exposes the listening ports of the container as they were services on the machine, so iptables doesn't do any mangling of traffic where to send connection to port XY to which container.

No that's not correct. You don't need to be in host mode to access the local LAN.

I know that in order to reach the local LAN I should configure the network mode to "host", is that correct?

No, that has nothing to do with that.

In that case am I still able to reach the other containers running in the default bridge network?

No, using network_mode host makes it more complicated to also reach other containers on the same Docker host.

Why not ask /r/Docker and read the Docker documentation?