First strange thing: with regard to the Cisco example you provided for other offices with similar setup - where all is OK - VLAN tagging/untagging can't be seen...so hard to tell you how Cisco trunked (AKA permitted VLANs passing on one interface...this in Cisco jargon) VLANs to related firewall and to downlinked other switch (there are two ports trunked 1/0/1 and 1/0/2)...so I can't do a 1:1 comparison to see how you setup...apart from that I'll concentrate on the HP scenario you're dealing with.
Probably you have:
Palo Alto firewall LAN port <---> port 22 (trk1) HP 2530-1 (trk2) port 23 <---> port x HP 2530-2
On HP-2530-1 port 3 there is a tag for VLAN 60 "DMZ_Network" (172.17.170.0/24 VLAN IP is 172.17.170.2) so I imagine that on port 3 there is something connected related to DMZ Network and that device is set to pass traffic TAGGED in VLAN 3 (so it understand VLAN tagging), probably a Server or a Switch setup accordingly.
On HP-2530-1 trk1 (port 22) and trk2 (port 23) are tagged on every VLAN you defined on the HP and are untagged member of VLAN 1...so I suspect that you are using both ports to transport those VLANs to Palo Alto and to the other HP Switch...which port do what you know, I just supposed that port 22 goes to Palo Alto and the other goes to the other HP...but it could be the contrary (it doesn't matter)...this means that trk1 and trk2 transport all your VLANs somewhere. Good.
Since IP routing is NOT enabled I then suspect that Palo Alto does IP routing for your setup...so its LAN port (facing the HP-2530-1 in my supposed topology) need to (a) be untagged in VLAN 1 (with compatible IP Addressing) and, concurrently, (b) be tagged for any VLAN you're trasporting to it (with compatible IP Addressing on each VLAN).
I then suspect that, since the Palo Alto is the default gateway for your network, then the 10.1.15.254 is its LAN port IP Address...but...in which VLAN? VLAN 99 or VLAN 1?
Looking at VLAN 99 I see ports 15, 17 and 19 untagged members of VLAN 99...so probably those are clients.
Looking at VLAN 1 I see ports 1-2, 4-14, 16, 18, 20, 21, 24-28, Trk1 and Trk2 as untagged members of VLAN 1...so I suspect that you're using that default gateway on VLAN 1 and so that IP addressing is valid for VLAN 1 (on HP and on Palo Alto LAN VLAN 1).
Now, if my picture is OK, this means that a client connected to, as example, on port 1 with an IP Address compatible with 10.1.15.254 (/24?) should ping your Palo Alto if its default gateway is set with 10.1.15.254 (which is the Palo Alto). Is this right?
Since you haven't on that HP access ports (for client hosts) on other VLANs than the VLAN 1, VLAN 60 and VLAN 99 then a step further would be test ping from port 3 (see above) or 15, 17, 19 (see above)...since VLAN 60 and VLAN 99 are transported (permitted) on trk1 (port 22) then a client on one of those ports (with the right client IP addressing) should be able to ping directly the Palo Alto IP Address(es) associated to the VLAN where the client is (and if the Palo Alto firewall inter-VLAN routing is configured accordingly also other VLAN IP address space). Does this happen?