you only add bridge1 interface to any interface list you might need (but for device to act as transparent gateway between local wired island and the rest of network via wireless hop you don’t need any interface lists IMO since you’re not using interface lists apart from incorrect use quoted above).
I also removed DHCP client from the wifi1 interface and made it a static address for management, since DHCP client was unhappy with a passthrough interface being bound to it, which is no big deal.
Final, working, config:
# 2024-01-15 10:47:36 by RouterOS 7.14beta6
# software id = WU29-BLCC
#
# model = C52iG-5HaxD2HaxD
# serial number = HEP08XS9X0H
/interface bridge
add name=bridge1
/interface wifi
set [ find default-name=wifi1 ] channel.band=5ghz-ax .frequency=5805 .skip-dfs-channels=all .width=20mhz configuration.country="United States" .mode=station-bridge .ssid=Hector disabled=no
/interface wifi security
add authentication-types=wpa3-psk disabled=no encryption=ccmp-256,gcmp-256 name=sec1
/system logging action
add email-to=noc@noc.com name=email target=email
/interface bridge port
add bridge=bridge1 interface=ether1
add bridge=bridge1 interface=ether2
add bridge=bridge1 interface=ether3
add bridge=bridge1 interface=ether4
add bridge=bridge1 interface=ether5
add bridge=bridge1 interface=wifi1
/ip firewall connection tracking
set udp-timeout=10s
/ipv6 settings
set disable-ipv6=yes
/ip address
add address=10.62.14.6/24 interface=wifi1 network=10.62.14.0
/system clock
set time-zone-name=America/New_York
/system identity
set name=livingroom-client-ap
/system logging
add action=email topics=critical,warning,account
/system note
set show-at-login=no
/system ntp client
set enabled=yes
/system ntp client servers
add address=10.62.14.1
/system package update
set channel=testing