Summary: It's a bug in servers, affecting all classes, introduced with the 25th Anniversary Update for Half-Life on November 17, 2023. Servers can switch to the steam_legacy beta to avoid it. Many already did, since this is the stable branch.

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I edited the map to allow other classes.
https://rv.apg-clan.org/dlds/strafe_tutorial_all_classes.zip

Tested:
- strafe_tutorial (civilian) worked fine with the steam_legacy beta.
- strafe_tutorial_all_classes (scout) also seemed ok with the steam_legacy beta.
- strafe_tutorial_all_classes (scout) accelerated way too much with regular TFC.
- strafe_tutorial (civilian) accelerated way too much with regular TFC.

So it seems that the map doesn't work with a regular TFC listen server (no matter which class), but works ok when using the steam_legacy beta for the listen server.

To opt into a beta, go to the Steam library, right click on TFC and choose properties.

Another affected map is rcramp. Normally you slide upwards all the way to the top. But with the current listen server, you get thrown to the top (as scout anyway). https://tfcmaps.net/?filterMap=rcramp

The same issue seems to apply to the current HLDS, though I didn't test it. Many servers use the steam_legacy beta instead since it's the stable version of HL and TFC. Add-ons like AMXX take this into account by staying compatible with this beta.

The current version of TFC is compatible with the legacy servers. So players can choose whether they want to use the current version or the steam_legacy beta.

Bug reports:
https://github.com/ValveSoftware/halflife/issues/3651
https://github.com/ValveSoftware/halflife/issues/3780
A TFC label has been added to these.

If SteamCMD is used to install and update the HLDS, here's a script for it to opt into the beta:
At least on Windows, you might have to let it run multiple times until it actually checks all data (>1GB).

Thank you so much for this reply. I was thinking maybe it was a custom air/ground friction setting on amx_mod that I would have to implement to fix it since most of the dedicated servers run that server mod for speedrun timers, checkpointing, etc. Thank you for providing me the workaround.