The only reasons to pick [Carrier] over other Sentinel companions are his high EHP, [Looter], and [Ammo Case], the issues with those reasons are:

At a high enough level, its EHP is meh.
An AoE weapon can fulfil [Looter]'s role
And You can fix your ammo issue elsewhere i.e:
Squad Ammo, Ammo mutation or Ammo Efficiency.

Don't take me wrong, [Carrier] ain't bad, but power creeps have made him kind of obsolete.

Flex

[Guardian]:
It's a must if you are using a shield gate for survival, else it's flex.

[Ammo Case]:
When you have solved your ammo issues somewhere else.

[Looter]:
QoL but not a must.

[Assault Mode]:
It's missing from the build as the damage your Companion does is negligible. That said, with the [Artax] you can have a permanent cold status on target, which can help with priming and CC

Not recommended

These mods are not bad, it's just that they do very little for a mod slot, that said, if u find yourself with mod slots open and u WANT what they do, go for them.

Repair Kit:
It takes 214 (1280 / 6) secs or 3 Mins and a half to fully heal Carrier.

Medi-Ray:
It heals 12% HP over 4s with a CD of 15 seconds -> 48% over a minute -> 0.8%/sec

Sanctuary:
Spoiler mode does the job better

Big no, unless you are over shielding/renewing shields, then yes.

[Calculated Redirection]:
It is arguably detrimental for survival if we take into consideration Shield Gating

Shields recharge at 15 units per second, plus 5% of the Warframe's maximum shields

Shield Recharge Rate = (15 + 0.05(Max Shield)) x (1 + Shield recharge Bonus)

Without [Calculated Redirection]

Shield Recharge Rate = (15 + 0.05(100)) x (1 + 0,9)
Shield Recharge Rate = (15 + 5) x (1,9)
Shield Recharge Rate = 38

100 / 38 ~ 2,6
3 seconds to recharge to the full gate.

With [Calculated Redirection]

Shield Recharge Rate = (15 + 0.05(375)) x (1 + 0,9)
Shield Recharge Rate = (15 + 0.05(375)) x (1 + 0,9)
Shield Recharge Rate = (15 + 18,75) x (1,9)
Shield Recharge Rate = 33,75 * 1,9
Shield Recharge Rate ~ 65

375 / 65 ~ 5,7
6 seconds to recharge to the full gate.