Recently I've discovered that "Staff Sergeant 1st Class" rank isn't actually final. There are Lieutenants, Captains and others. I suppose I can reach them, but how can I make bots spawn with them too?

Right now you can't. It's hardcoded in the game that AI spawns randomly with 0.0 - 0.5 authority mapping to 0 - 5000 XP. The problem is mainly that with the current logic, the probability to spawn a soldier with 1000XP and with 9000XP would be exactly same, so there would be an equal amount of low rank soldiers and high rank officers, causing issues with forming squads.

There will be at least some way to influence this in the future versions as vanilla will need it as well.

<rank xp="0.0" name="Private">
<hud_icon filename="hud_rank0.png" />
</rank>
<rank xp="0.05" name="Private 1st Class">
<hud_icon filename="hud_rank1.png" />
</rank>
<rank xp="0.1" name="Corporal">
<hud_icon filename="hud_rank2.png" />
</rank>
<rank xp="0.15" name="Sergeant">
<hud_icon filename="hud_rank3.png" />
</rank>
<rank xp="0.2" name="Staff Sergeant">
<hud_icon filename="hud_rank4.png" />
</rank>
<rank xp="0.25" name="Staff Sergeant 1st Class">
<hud_icon filename="hud_rank5.png" />
</rank>
<rank xp="0.3" name="2nd lieutenant">
<hud_icon filename="hud_rank6.png" />
</rank>
<rank xp="0.35" name="Lieutenant">
<hud_icon filename="hud_rank7.png" />
</rank>
<rank xp="0.4" name="Captain">
<hud_icon filename="hud_rank8.png" />
</rank>
<rank xp="0.45" name="Major">
<hud_icon filename="hud_rank9.png" />
</rank>
<rank xp="0.5" name="Lieutenant Colonel">
<hud_icon filename="hud_rank10.png" />
</rank>
<rank xp="0.55" name="Colonel">
<hud_icon filename="hud_rank11.png" />
</rank>
<rank xp="0.6" name="Brigadier General">
<hud_icon filename="hud_rank12.png" />
</rank>
<rank xp="0.7" name="Major General">
<hud_icon filename="hud_rank13.png" />
</rank>
<rank xp="0.8" name="Lieutenant General">
<hud_icon filename="hud_rank14.png" />
</rank>
<rank xp="0.9" name="General">
<hud_icon filename="hud_rank15.png" />
</rank>
<rank xp="1.0" name="General of the Army">
<hud_icon filename="hud_rank16.png" />
</rank>

All bots currently spawn with 0 - 5000 XP. They do gain experience, but they don't survive as long as to gain it in significant amounts. Respawning bot is always a completely new one, again getting random starting XP between 0 - 5k.

In 0.95/probably next patch the soldier group within faction -feature will be expanded, so that we can control distribution of bot XP and define very high XP bots to appear in the game very rarely, with special equipment.