There are actually more properties available for info_player_teamspawn than are listed here. If you look at the changelog for the Team Fortress Classic.fgd entity definition file at https://developer.valvesoftware.com/wiki/Team_Fortress_Classic.fgd there's a change which reads
"Removed TFCriteria and TFEffects5 from info_player_teamspawn and moved relevant properties to TFSpawnInfo."
I'm not sure what the owner of that comment considered relevant, but TFEffects5 includes things like...
and more, but those are the especially relevant ones I saw. These are all available and will work just fine on info_player_teamspawn, but since the TFEffects5 associated was removed in the .fgd they won't show up by default in mapping tools like JACK or TrenchBroom.
If you look at the changelog for the Team Fortress Classic.fgd entity definition file at https://developer.valvesoftware.com/wiki/Team_Fortress_Classic.fgd there's a change which reads I'm not sure what the owner of that comment considered relevant, but TFEffects5 includes things like...
armorvalue (Armor Value %)
a_s (Add/Subtract shells)
a_n (Add/Subtract nails)
a_r (Add/Subtract rockets)
a_c (Add/Subtract cells)
ammo_detpack (Add/Subtract detpack)
no_grenades_1 (Add/subtract grenades #1)
no_grenades_2 (Add/subtract grenades #2)