FWIW, I have a similar set up and it works perfectly. What nightly build of Lineage-18.1 are you using?
Seems to be something in your new install doesn't play well with your current Lineage build.
As an aside, the Lineage team appears to have removed nightly 18.1 series. Perhaps, an upgrade to 19.1 (Android 12) which is compatible with Pixel 3, might work.

My setup:
- Slackware 15.0 (kernel 5.15.38 huge)
- Pixel 3(blueline)
- Lineage OS 18.1 (lineage-18.1-20220412-nightly-blueline and I recently updated to lineage-18.1-20220420
- Both nightly versions - 20220412 and 20220420 - connect perfectly with Slackware 15.0 and I'm able to transfer files etc.
- I have a single network wireless rule, in /etc/udev/rules.d and nothing else. No rules for Pixel3 (or my Samsung Galaxy S5 for that matter, both work)

Listing some output and including loaded modules filtered for USB.
------------------------------------------------------------------
$ tail -50 /var/adm/message
Jun 20 20:00:57 rover kernel: usb 2-5: new high-speed USB device number 3 using ehci-pci
Jun 20 20:00:57 rover kernel: usb 2-5: New USB device found, idVendor=18d1, idProduct=4ee7, bcdDevice= 4.40
Jun 20 20:00:57 rover kernel: usb 2-5: New USB device strings: Mfr=1, Product=2, SerialNumber=3
Jun 20 20:00:57 rover kernel: usb 2-5: Product: Pixel 3
Jun 20 20:00:57 rover kernel: usb 2-5: Manufacturer: Google

$ lsusb
Bus 002 Device 003: ID 18d1:4ee7 Google Inc. Nexus/Pixel Device (charging + debug)
Bus 002 Device 002: ID 058f:6362 Alcor Micro Corp. Flash Card Reader/Writer
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 008 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 007 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 006 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 005 Device 003: ID 046d:c018 Logitech, Inc. Optical Wheel Mouse
Bus 005 Device 002: ID 04f2:0841 Chicony Electronics Co., Ltd HP Multimedia Keyboard

$ lsmod | grep usb
snd_usb_audio 327680 1
snd_usbmidi_lib 36864 1 snd_usb_audio
snd_rawmidi 40960 1 snd_usbmidi_lib
mc 57344 1 snd_usb_audio
usbhid 57344 0
hid 143360 2 usbhid,hid_generic
usb_storage 77824 1 uas
snd_hwdep 16384 2 snd_usb_audio,snd_hda_codec
snd_pcm 143360 5 snd_hda_codec_hdmi,snd_hda_intel,snd_usb_audio,snd_hda_codec,snd_hda_core
snd 106496 22 snd_hda_codec_generic,snd_seq_device,snd_hda_codec_hdmi,snd_hwdep,snd_hda_intel,snd_usb_audio,snd_us bmidi_lib,snd_hda_codec,snd_hda_codec_realtek,snd_timer,snd_pcm,snd_rawmidi