the count of messages is somehow exposed in the proc filesystem
No, there's nothing like that.
dmesg --level=emerg,alert,crit,err vs "It would be great to give an indication of hardware issues."
Messages under these log levels are not necessarily indicative of hardware issues.
Here's what I get:
Speculative Return Stack Overflow: WARNING: kernel not compiled with MITIGATION_SRSO.
Hangcheck: starting hangcheck timer 0.9.1 (tick is 180 seconds, margin is 60 seconds).
systemd[1]: Failed to find module 'autofs4'
systemd[1]: systemd-journald.service: unit configures an IP firewall, but the local system does not support BPF/cgroup firewalling.
systemd[1]: systemd-journald.service: (This warning is only shown for the first unit using IP firewalling.)
nvidia: loading out-of-tree module taints kernel.
iwlwifi 0000:04:00.0: WRT: Overriding region id 0
iwlwifi 0000:04:00.0: WRT: Overriding region id 1
iwlwifi 0000:04:00.0: WRT: Overriding region id 2
iwlwifi 0000:04:00.0: WRT: Overriding region id 3
iwlwifi 0000:04:00.0: WRT: Overriding region id 4
iwlwifi 0000:04:00.0: WRT: Overriding region id 6
iwlwifi 0000:04:00.0: WRT: Overriding region id 8
iwlwifi 0000:04:00.0: WRT: Overriding region id 9
iwlwifi 0000:04:00.0: WRT: Overriding region id 10
iwlwifi 0000:04:00.0: WRT: Overriding region id 11
iwlwifi 0000:04:00.0: WRT: Overriding region id 15
iwlwifi 0000:04:00.0: WRT: Overriding region id 16
iwlwifi 0000:04:00.0: WRT: Overriding region id 18
iwlwifi 0000:04:00.0: WRT: Overriding region id 19
iwlwifi 0000:04:00.0: WRT: Overriding region id 20
iwlwifi 0000:04:00.0: WRT: Overriding region id 21
iwlwifi 0000:04:00.0: WRT: Overriding region id 28
NVRM: loading NVIDIA UNIX Open Kernel Module for x86_64 565.77 Release Build (dvs-builder@U16-A21-31-3) Wed Nov 27 23:09:12 UTC 2024
FAT-fs (nvme0n1p1): utf8 is not a recommended IO charset for FAT filesystems, filesystem will be case sensitive!
Bluetooth: hci0: HCI LE Coded PHY feature bit is set, but its usage is not supported.
block nvme0n1: No UUID available providing old NGUID
VBoxNetFlt: Successfully started.
VBoxNetAdp: Successfully started.
A warning from the BlueTooth module is the only one that's related to HW.