I was just about to destroy my proxmox lab and start all over again until I saw your question. Maybe we can help each other? I'm new to Proxmox as well and having this same problem as well: My proxmox host has no Internet access, yet my VMs and containers (pfSense, Ubuntu Servers, Docker and Portainer) all have Internet access.
Below are the things I've checked so far along with my results so you can compare. Hopefully we can resolve this issue:
0) I ssh into Proxmox
	
	
1) Ping Google (unsuccessful)
	
	
 
2) Ping 8.8.8.8 (unsuccessful)
	
	
3) Ping my ISP's internet router (success!)
	
	
4) Traceroute (All "***", from 1 to 30)
	
	
5) Nslookup (REFUSED)
	
	
	
		Code:
	
	
		nslookup 8.8.8.8 #** server can't find 8.8.8.8.in-addr.arpa: REFUSED
	 
 
6) nslookup (REFUSED)
	
	
	
		Code:
	
	
		nslookup google.com
Server:        192.168.100.1
Address:    192.168.100.1#53
** server can't find google.com: REFUSED
	 
 
7) ip route
	
	
	
		Code:
	
	
		ip route
default via 192.168.100.1 dev vmbr0 proto kernel onlink
10.10.1.0/24 dev vmbr1 proto kernel scope link src 10.10.1.0
192.168.100.0/24 dev vmbr0 proto kernel scope link src 192.168.100.100
	 
 
8) DNS config
	
	
	
		Code:
	
	
		cat /etc/resolv.conf
nameserver 192.168.100.1
nameserver 8.8.8.8
	 
 
9) I changed my Proxmox host IP to 192.168.100.100
10) Hosts lookup table
	
	
	
		Code:
	
	
		cat /etc/hosts
127.0.0.1 localhost.localdomain localhost
192.168.100.100 lab.local lab
	 
 
11) Interfaces
	
	
	
		Code:
	
	
		cat /etc/network/interfaces
auto lo
iface lo inet loopback
iface enp0s31f6 inet manual
auto vmbr0
iface vmbr0 inet static
    address 192.168.100.100/24
    gateway 192.168.100.1
    bridge-ports enp0s31f6
    bridge-stp off
    bridge-fd 0
iface wlp4s0 inet manual
auto vmbr1
iface vmbr1 inet static
    address 10.10.1.0/24
    bridge-ports none
    bridge-stp off
    bridge-fd 0
    bridge-vlan-aware yes
    bridge-vids 2-4094
#LAB LAN
source /etc/network/interfaces.d/*
	 
 
12) Proxmox firewall status
	
	
	
		Code:
	
	
		pve-firewall status # Status: enabled/running
cat /etc/pve/firewall/cluster.fw # (enable: 1)
	 
 
Note: there were no firewall rules in my cluster.fw
13) Firewall rules in output chain related to proxmox 192.168.100.100
	
	
	
		Code:
	
	
		iptables -L OUTPUT -v -n | grep '192.168.100.100' # no results found
iptables -L -v -n # Lots of rules but can't figure it out yet
	 
 
14) My ISP's Internet router's DHCP range is from 192.168.100.2 to 192.168.100.254 and no other device is using my proxmox IP (192.168.100.100)
15) I'm carefully going through Dunuin's comment from another post:
	
	
	
		Code:
	
	
		What does your network configuration look like (cat /etc/network/interfaces, cat /etc/hosts, cat /etc/resolv.conf)? Did you make sure the gateway and DNS server is setup correctly?
When guests can go online but the host not, its usually either:
1.) wrong gateway
2.) wrong DNS server
3.) double use of IPs, IP already used by another host
4.) host got 2 IPs in the same subnet
5.) using a IP of a wrong subnet
6.) bad firewall rules
	 
 
EDIT: 16) When i checked the DNS on my laptop, I get a different nameserver
	
	
	
		Code:
	
	
		nameserver 127.0.0.53
options edns0 trust-ad
search .