Revert "Reland "Send first probe packet directly instead of enqueuing it.""

This reverts commit 1386fbca8b558f14336d9863c8a4e8f2654ab568.

Reason for revert: Now another downstream test flakes :(

Original change's description:
> Reland "Send first probe packet directly instead of enqueuing it."
>
> This is a reland of commit 8088aad5ac0154d8fdc252de9e8ab4e0172d7da2
>
> Original change's description:
> > Send first probe packet directly instead of enqueuing it.
> >
> > This avoids potentially creating needless containers in the packet
> > queue and removes usage of the packet prio, allowing it to be moved in
> > an upcoming CL.
> >
> > Bug: webrtc:11340
> > Change-Id: Iddd9e7e4e73c97ab25a85e42bcc0094d61fd60d3
> > Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/259524
> > Reviewed-by: Emil Lundmark <lndmrk@webrtc.org>
> > Commit-Queue: Erik Språng <sprang@webrtc.org>
> > Cr-Commit-Position: refs/heads/main@{#36602}
>
> Bug: webrtc:11340
> Change-Id: I3e0db452961f7f5a8d00ea3283e92ec43da2f66a
> Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/259774
> Reviewed-by: Emil Lundmark <lndmrk@webrtc.org>
> Commit-Queue: Erik Språng <sprang@webrtc.org>
> Cr-Commit-Position: refs/heads/main@{#36619}

Bug: webrtc:11340
Change-Id: I31b2c6636aca5debe8e4d71546b5a3b9eb746c9d
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/259862
Auto-Submit: Erik Språng <sprang@webrtc.org>
Reviewed-by: Erik Språng <sprang@webrtc.org>
Commit-Queue: Erik Språng <sprang@webrtc.org>
Bot-Commit: rubber-stamper@appspot.gserviceaccount.com <rubber-stamper@appspot.gserviceaccount.com>
Commit-Queue: rubber-stamper@appspot.gserviceaccount.com <rubber-stamper@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/heads/main@{#36620}