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.