There is too many factors involved here and there is no way we can even suggest what could be wrong.
Start with big entry point - you ISP - ensure you use a port your ISP has configured for initernet which appears to be working judging from your output.
2: ens5f5: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc fq_codel state UP group default qlen 1000
link/ether bc:ae:c5:a3:3f:4e brd ff:ff:ff:ff:ff:ff promiscuity 0 minmtu 1280 maxmtu 9202 numtxqueues 1 numrxqueues 1 gso_max_size 65536 gso_max_segs 65535 parentbus pci parentdev 0000:04:00.5
altname enp4s0f5
inet 192.168.1.204/24 brd 192.168.1.255 scope global dynamic noprefixroute ens5f5
valid_lft 86391sec preferred_lft 86391sec
inet6 2001:b07:ac9:3ecd:cd51:7caa:8866:f08a/64 scope global dynamic noprefixroute
valid_lft 86396sec preferred_lft 86396sec
inet6 fe80::b299:d1b0:76db:f5e9/64 scope link noprefixroute
valid_lft forever preferred_lft forever
If your connection is up - as indicated - but you cannot connect - then the dns resolver on this particular system is not setup correct.
Ensure your testing cable works - then move outwards one point at a time - when the connection fails you have your faulty port/device.
Another possibility is address collision ensure that you know each assigned address if any and that no system is using a fixed IP in a DHCP range.
It is important that you - at every checkpoint - is thorough and methicolous in your testing. Make a checklist whatever works for you and ensure you go over each item at every checkpoint.
A last thought - when it connects when you connect directly to the ISP provided equipment - at least thats how I understand you issue - it could be a negotiation problem or perhaps a switch mac address assignment which is bugging you.
On method I have used over the years to eliminate problem junctions is to remove power from all equipment for a couple of minutes - then power on starting with the entry point.
Searching for
JMicron JMC250 PCI Express Gigabit Ethernet
shows a lot of issues over the years with this specific chipset.
Your device firmware is dating back 10 years - it is next to impossible to suggest what to do - one would think they got it right at some point.
There is hardware which have the most peculiar behavior under Linux yet using Windows there’s no issues. I thinkt that is because not all hardware is create with Linux in mind - especially not old hardware such as this laptop.