Looking at the Commanders individually, here's my outlook on how naturally Zirda as a Companion can fit into most builds and whether it's worth it to build them with Zirda in general. This is to help narrow down possible directions you can take to use Zirda as a Companion.
Underpowered:
All of these commanders are either weak or unexciting compared to other commanders in the same colours (pretty much all of the Boros commanders, Cromat, Licia), are part of a creature tribe or use a mechanical space that include too many (necessary) cards that lack activated abilities (Tazri, Scion, Horde, Mayael), or are a huge meme (Atogatog).
Playable:
These cards have no direct synergy with Zirda but at least have the potential to support possible reasonably strong builds for them. Basandra seems the best of the Boros commanders for a potential equipment/creature ability based deck, Tariel and Kelsien both benefit from being untapped via
Thousand-Year Elixir and friends, the Shark companion seems like one of the better possible homes for a cycling deck using Zirda, and Atla, Zedruu, and all of the 5C commanders are open and powerful enough that you could build them however you want within the restriction and have Zirda support you for it.
Good Potential:
Each of these is either a commander that directly benefits from the mana discount or is known for playing cards that fit the requirement, though ultimately the stronger build for these generals likely won't Companion Zirda. They can definitely still be fun and powerful though.
Kykar can be played almost permanentless to begin with, so having an extra card to enable combos or make certain cards more efficient is swell. You still have access to
Purphoros, God of the Forge,
Goblin Bombardment,
Skullclamp,
Metallurgic Summonings, as well as the new Sharknado. Likely still not optimal but you could build it.
Akim has a lot of token makers that use activated abilities (
Faerie Formation,
Heliod, God of the Sun,
Dawn of Hope) so reducing those costs to more efficiently make tokens off their trigger is pretty strong. Reducing that expensive-arse double strike ability helps a bit too. Not being able to play most anthem effects is a bummer though - you'll have to stick to spell-based pump or cards like
Leonin Sun Standard. This deck definitely uses Zirda better than Kykar, even if the average Kykar deck is probably stronger.
Samut is often built as activated ability tribal so Zirda is just a natural fit. Zacama getting reduced to 1 mana activations is quite crazy, but without mana doublers you lack a bit of oomph.
Marath is just made so much more efficient by Zirda, and while I don't think there are any obvious combos you can do with the restriction, that's OK by me. You do lose out on
Doubling Season and some other cards that are naturally good in the deck, but if you're using Marath more as a control tool Zirda seems like it should help a lot.
Sisay can still play Planeswalkers alongside
Rhys the Redeemed and whatever other strong legends have activated abilities, but you are losing out on a lot of cards and you probably aren't using Zirda very well. I could see this still being reasonably strong.
High Synergy:
These guys all seem insane, mostly because they gain significant discounts from Zirda and can be easily built to accommodate her.
Training Grounds is one of the better cards in Kenrith, and having it in the Companion zone lets you cheat on mana pretty drastically. Golos getting a discount is less relevant, but you can build Golos however you want so Zirda will always be extremely helpful to your strategy. Breya generally plays with a lot of artifacts which tend to use activated abilities naturally, and reducing those costs is something we've never had access to on this scale; there's definitely shenanigans to be had there, more than just
Grim Monolith or
Basalt Monolith.
These are just my initial thoughts, LMK if I missed any synergies that make any of these options more viable.
Zacama
Just ideas.
