If there is 40% neon or neon-helium in argon in T5 HO, why I've never seen a red glow discharges at the ends of them?

looking at an official manufacturing chart I happen to have for the fill gas and pressures of T5 tubes, only the 24W and 39W HO types are Half Neon filled, the 54W 49W and 80W are still Pure Argon, and I think most of the T5 HO tubes you have looked at have been 54W ones?

(although of course there could still be manufacture to manufacture variation)

700-series should still be relatively easy to find in all of the typical places, they were super popular. They haven’t been made in over 10 years though, so supply is limited. You should probably be able to find them online pretty easily, though the prices will most likely be astronomical. It might be worth checking your local small hardware store if you have one, my local Ace still has some GE F32T8/SP41s in stock. As for halophosphate, these are super rare. Sylvania made them for a brief time in the early 2010s in response to a triphosphor shortage, but the bans that took place shortly after meant they had to be discontinued. GE also made deluxe halophosphate F32T8s, those were made for an extended period, so they are slightly more common. But all of these F32T8 halophosphate lamps are pretty rare and are probably not something that could be found on demand.

Finished reassembling a vintage fluorescent desk lamp I started restoring last week.

Stumbled upon a house clearing and grabbed a box of random lamps, there's some halogens and incandescents mixed with CFLs and the usual crap LED I'll just resell, if they even work, same with the CFLs, pretty sure they're all 6500K so I won't keep any. It's pretty dusty so I didn't really see what exactly the lamps are yet.

Also grabbed a box fan, 2 floor lamps and an alarm clock, $5 for the bunch, guy wanted $10 but the lamps have broken holders and are overall super loose, and the fan is missing the timer knob. Not sure if the alarm clock even works but there's tape on the cord, so that has to be fixed as well.

Usually because there is mercury vapour present and its discharge colour overpowers that of the gasfilling.  If you place the lamp in a freezer below about -40C and remove the mercury vapour, and ionise the gas filling not too strongly, then you can see the neon discharge colour.

If there is 40% neon or neon-helium in argon in T5 HO, why I've never seen a red glow discharges at the ends of them?

There are so many different fills, but the following basic listing is approximately correct for most manufacturers as far as I know:

T12, T8 and T5 standard : Pure argon, or sometimes argon with a very small percentage of neon and/or helium to tweak the voltage slightly.  The main exception is the British T12 8ft 100W which contains approx 25% Krypton in Argon.

T8 European energy saving tubes: Nearly all 25% Krypton, 75% Argon

T8 European extra energy saving: Still mainly argon but with varying percentages of krypton and/or even xenon.

T12 American energy saving tubes: Nearly all between 10-40% Krypton in Argon.

T12 High Output: Argon, sometimes with very small trace of neon or helium

T12 Very High Output: Usually Argon with quite high percentage of Neon and/or Helium, to raise the voltage drop and facilitate high power dissipation from low current cathodes, while also improving efficacy under high discharge current conditions.

T5 Long High Efficacy : Usually pure argon for the short tubes, and argon with between about 3% and 11% Krypton for the longer lamps.

T5 Long High Output : Argon with up to about 40% neon or neon-helium added in varying quantities, for similar reasons as in T12 VHO types.

T5 low current emergency lighting types : Argon + small amount of carbon dioxide

In all cases the pressure is low, usually between about 1 and 4 torr.  There is not a consistent trend of pressure per lamp type, this can depend on the tube length / current rating.

I've noticed that the Philips SDW-T and SDW-TG, tends to rectify during starting, even when new.
Why this is happening?

I bought it at Machsanei Teura lighting store.

That sounds good. Where did you get your track light?