iptables: why are outgoing connections working even though no rules allow it

The INPUT and OUTPUT chain policies are set to DROP. Very few rules allowing only specific traffic between directly cable-connected devices. However, if I temporarily add a cable that goes to the router, why can I initiate outgoing connections and receive answers, like do apt update, even though there are no rules allowing HTTP traffic in our out?

I have noticed that if I add iptables -P FORWARD DROP then those outgoing connections don't work anymore. Why does the FORWARD chain have any impact in this?

raspberrypi:~ $ sudo iptables -nvL
Chain INPUT (policy DROP 332 packets, 244K bytes)
 pkts bytes target     prot opt in     out     source               destination         
    0     0 ACCEPT     all  --  lo     *       0.0.0.0/0            0.0.0.0/0           
 1254 79084 ACCEPT     tcp  --  *      *       66.66.66.5           66.66.66.3           tcp dpt:21385 ctstate NEW,ESTABLISHED
 1453 2495K ACCEPT     all  --  *      *       0.0.0.0/0            0.0.0.0/0            ctstate RELATED,ESTABLISHED

Chain FORWARD (policy ACCEPT 0 packets, 0 bytes)
 pkts bytes target     prot opt in     out     source               destination         

Chain OUTPUT (policy DROP 373 packets, 47731 bytes)
 pkts bytes target     prot opt in     out     source               destination         
 1715  162K ACCEPT     tcp  --  *      *       99.99.99.3           99.99.99.2           tcp dpt:5656
    6   456 ACCEPT     udp  --  *      *       99.99.99.3           99.99.99.2           udp dpt:123
  952  156K ACCEPT     all  --  *      *       0.0.0.0/0            0.0.0.0/0            ctstate RELATED,ESTABLISHED

Secondary question: Is there any risk in using those easy to recognize IP addresses between my internally and directly cable-connected devices? Could packets leak, because those are valid public addresses?

EDIT: adding requested info.

We are talking about the device "Raspi Client".

Output of iptables-save:

raspberrypi:~ $ sudo iptables-save
# Generated by xtables-save v1.8.2 on Wed Jan 19 10:42:58 2022
*nat
:PREROUTING ACCEPT [529:48304]
:INPUT ACCEPT [7:420]
:POSTROUTING ACCEPT [2465:187164]
:OUTPUT ACCEPT [2804:242065]
:DOCKER - [0:0]
-A PREROUTING -m addrtype --dst-type LOCAL -j DOCKER
-A POSTROUTING -s 172.17.0.0/16 ! -o docker0 -j MASQUERADE
-A OUTPUT ! -d 127.0.0.0/8 -m addrtype --dst-type LOCAL -j DOCKER
-A DOCKER -i docker0 -j RETURN
COMMIT
# Completed on Wed Jan 19 10:42:58 2022
# Generated by xtables-save v1.8.2 on Wed Jan 19 10:42:58 2022
*filter
:INPUT DROP [607:267621]
:FORWARD ACCEPT [0:0]
:OUTPUT DROP [394:50896]
-A INPUT -i lo -j ACCEPT
-A INPUT -s 66.66.66.5/32 -d 66.66.66.3/32 -p tcp -m tcp --dport 21385 -m conntrack --ctstate NEW,ESTABLISHED -j ACCEPT
-A INPUT -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT
-A OUTPUT -s 99.99.99.3/32 -d 99.99.99.2/32 -p tcp -m tcp --dport 5656 -j ACCEPT
-A OUTPUT -s 99.99.99.3/32 -d 99.99.99.2/32 -p udp -m udp --dport 123 -j ACCEPT
-A OUTPUT -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT
COMMIT
# Completed on Wed Jan 19 10:42:58 2022

INPUT and OUTPUT chains cover for communication where the source or destination of the traffic is the router itself.

FORWARD covers the traffic that the router forwards from one interface to another (from LAN port to WAN port and vice versa.