Bluetooth keyboard input lag? (goes away if bluetooth mouse disconnected) Ubuntu 22.04

I have a lagging problem with a bluetooth keyboard which I can only reproduce by using my computer for enough time (some tens or hundreds of minutes).

Symptoms:

• The keyboard starts to have significant input lag: The characters come even seconds later the keys have been pressed, and some characters may be even lost.
• This seems to affect all programs (terminal, browser, notepadqq,..)

System & HW:

• Ubuntu 22.04.2 LTS (Jammy Jellyfish) running on HP Elitebook laptop
• Mouse: Microsoft Surface Mouse (Which based on Google search uses Bluetooth 4.0)
• Keyboard: MX Keys Mini (Which based on Google search uses Bluetooth 5.0)
• The bluetooth receiver is built in (inside the laptop), using Bluetooth version 4.2.

Debugging details:

I have found out, that when the lagging starts

• Shutting down the mouse with it's power button will remove the keyboard lag temporarily. The keyboard starts lagging again if mouse is powered again (and reconnected).
• Rebooting the keyboard will remove the keyboard lag (semi-)permanently (i.e. until the problem occurs again).

Here's also some dmesg output with my comments starting with --- :

$ sudo dmesg
...
[222409.820139] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000D/input/input80
[222409.820356] input: Surface Mouse Consumer Control as /devices/virtual/misc/uhid/0005:045E:0919.000D/input/input81
[222409.820493] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000D/input/input82
[222409.820698] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000D/input/input83
[222409.820880] hid-generic 0005:045E:0919.000D: input,hidraw1: BLUETOOTH HID v1.32 Mouse [Surface Mouse] on 20:16:b9:d1:54:97
[222412.747962] input: MX Keys Mini Keyboard as /devices/virtual/misc/uhid/0005:046D:B369.000E/input/input85
[222412.749122] hid-generic 0005:046D:B369.000E: input,hidraw2: BLUETOOTH HID v0.04 Keyboard [MX Keys Mini] on 20:16:b9:d1:54:97
--- No problems here yet (starts somewhere down below, before 233992)
[222575.313702] input: Bose QC35 (AVRCP) as /devices/virtual/input/input87
[228493.379991] audit: type=1326 audit(1681644183.335:78): auid=1000 uid=1000 gid=1000 ses=2 subj=snap.snap-store.ubuntu-software pid=60040 comm="snap-store" exe="/snap/snap-store/638/usr/bin/snap-store" sig=0 arch=c000003e syscall=314 compat=0 ip=0x7f68cfea473d code=0x50000
[229528.103666] Lockdown: systemd-logind: hibernation is restricted; see man kernel_lockdown.7
[229528.110186] Lockdown: systemd-logind: hibernation is restricted; see man kernel_lockdown.7
[229553.586035] Lockdown: systemd-logind: hibernation is restricted; see man kernel_lockdown.7
[229553.590070] Lockdown: systemd-logind: hibernation is restricted; see man kernel_lockdown.7
[229972.672035] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000F/input/input88
[229972.672527] input: Surface Mouse Consumer Control as /devices/virtual/misc/uhid/0005:045E:0919.000F/input/input89
[229972.672736] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000F/input/input90
[229972.672934] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.000F/input/input91
[229972.673168] hid-generic 0005:045E:0919.000F: input,hidraw1: BLUETOOTH HID v1.32 Mouse [Surface Mouse] on 20:16:b9:d1:54:97
[230011.566777] hp_wmi: Unknown event_id - 131073 - 0x0
--- The mouse was manually restarted here
[232350.405006] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.0010/input/input93
[232350.405835] input: Surface Mouse Consumer Control as /devices/virtual/misc/uhid/0005:045E:0919.0010/input/input94
[232350.406148] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.0010/input/input95
[232350.406466] input: Surface Mouse as /devices/virtual/misc/uhid/0005:045E:0919.0010/input/input96
[232350.406924] hid-generic 0005:045E:0919.0010: input,hidraw1: BLUETOOTH HID v1.32 Mouse [Surface Mouse] on 20:16:b9:d1:54:97
--- restart keyboard -> fixes the problem
[233992.420235] input: MX Keys Mini Keyboard as /devices/virtual/misc/uhid/0005:046D:B369.0011/input/input98
[233992.420490] hid-generic 0005:046D:B369.0011: input,hidraw2: BLUETOOTH HID v0.04 Keyboard [MX Keys Mini] on 20:16:b9:d1:54:97

Bluetooth receiver

niko@niko-ubuntu-home:/var/tmp$ hciconfig -a
hci0:   Type: Primary  Bus: USB
    BD Address: 20:16:B9:D1:54:97  ACL MTU: 1021:4  SCO MTU: 96:6
    UP RUNNING PSCAN ISCAN INQUIRY 
    RX bytes:91026274 acl:1090853 sco:13012 events:2628087 errors:0
    TX bytes:166701082 acl:266103 sco:11767 commands:509565 errors:0
    Features: 0xff 0xfe 0x0f 0xfe 0xdb 0xff 0x7b 0x87
    Packet type: DM1 DM3 DM5 DH1 DH3 DH5 HV1 HV2 HV3 
    Link policy: RSWITCH HOLD SNIFF 
    Link mode: PERIPHERAL ACCEPT 
    Name: 'niko-ubuntu-home'
    Class: 0x7c010c
    Service Classes: Rendering, Capturing, Object Transfer, Audio, Telephony
    Device Class: Computer, Laptop
    HCI Version: 4.2 (0x8)  Revision: 0x100
    LMP Version: 4.2 (0x8)  Subversion: 0x100
    Manufacturer: Intel Corp. (2)

Question:

Why would a connected bluetooth mouse make a bluetooth keyboard lag? How can I fix or debug this..?