`zsh` and `bash` handle command output differently

Question

In zsh:

% RESPONSE=$(ping -c 1 raspberrypi4b.local)
% echo $RESPONSE | grep "% packet loss" 
1 packets transmitted, 1 packets received, 0.0% packet loss

But in bash it's different:

$ RESPONSE=$(ping -c 1 raspberrypi4b.local)
$ echo $RESPONSE | grep "% packet loss"
PING raspberrypi4b.local (192.168.1.184): 56 data bytes 64 bytes from 192.168.1.184: icmp_seq=0 ttl=64 time=1.376 ms --- raspberrypi4b.local ping statistics --- 1 packets transmitted, 1 packets received, 0.0% packet loss round-trip min/avg/max/stddev = 1.376/1.376/1.376/0.000 ms

Yet when I run ping directly, the output is formatted identically:

In zsh:

% ping -c 1 raspberrypi4b.local
PING raspberrypi4b.local (192.168.1.184): 56 data bytes
64 bytes from 192.168.1.184: icmp_seq=0 ttl=64 time=7.526 ms

--- raspberrypi4b.local ping statistics ---
1 packets transmitted, 1 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 7.526/7.526/7.526/0.000 ms

in bash:

$ ping -c 1 raspberrypi4b.local
PING raspberrypi4b.local (192.168.1.184): 56 data bytes
64 bytes from 192.168.1.184: icmp_seq=0 ttl=64 time=7.613 ms

--- raspberrypi4b.local ping statistics ---
1 packets transmitted, 1 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 7.613/7.613/7.613/0.000 ms

It seems that bash is ignoring the newlines that are in the output of ping, but perhaps the variable assignment has caused this? In either case, can I get bash to handle this string in the same way that zsh does?