So a couple of thought I have in terms of adjusting the rune knight.
1) I don't like the crossover between the fighter and barbarian rage. I also don't agree with the runes being level-gated. They should all be within the same relative power scale. So here are a couple of the runes I have re-worked.
Frost Rune. This rune's magic evokes the might of those who survive in the wintry wilderness, such as frost giants. While wearing or carrying an object inscribed with this rune, you have advantage on Animal Handling and Intimidation checks.
In addition, you can invoke the rune as a bonus action to increase your sturdiness. For 10 minutes, you gain a bonus to all ability checks and saving throws that use Strength or Constitution. This bonus is equal to your proficiency bonus. Once you invoke this rune, you can't do so again until you finish a short or long rest.
Hill Rune. This rune's magic bestows a resilience reminiscent of a hill giant. While wearing or carrying an object that bears this rune, you have advantage on saving throws against being poisoned, and you have resistance against poison damage.
In addition, you can invoke the rune as a bonus action. For the next minute, you reduce any damage you take by an amount equal to your proficiency bonus. Once you invoke this rune, you can't do so again until you finish a short or long rest.
Changes: So I buffed the Frost Rune a bit to raise it on par with the other runes. I also adjusted the Hill Rune to be more similar to the Heavy Armor Master feat than barbarian rage.
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2) I also feel like the Runic Shield ability is a bit too similar to the Storm Rune. I also think the Storm Rune is a bit too powerful. Additionally, as others have noted, the limit with bonus actions does cause the Rune Knight to take a bit to get going. So below is my proposed swap for Runic Shield and my adjustment to the Storm Rune.
Runic Growth
7th-level Rune Knight feature
Whenever you activate one of your runes, you can also activate your Giant’s Might feature with the same action.
Storm Rune. Using this rune, you can glimpse the future like a storm giant seer. While wearing or carrying an object inscribed with this rune, you have advantage on Arcana checks, and you can't be surprised as long as you aren't incapacitated.
In addition, you can invoke the rune as a bonus action to enter a prophetic state for 1 minute or until you're incapacitated. Until the state ends, when you or another creature you can see within 60 feet of you makes an attack roll, a saving throw, or an ability check, you can use your reaction to increase or decrease the roll by an amount equal to your proficiency bonus. Once you invoke this rune, you can't do so again until you finish a short or long rest.
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3) This is more of a minor gripe, but I feel like Giant's Might should recharge on a short rest mechanic rather than a long rest one. This is not a long rest based archetype. I also don't like the idea of granting these kinds of abilities based on proficiency bonus. I like multiclassing, and while I think some abilities should continue to scale regardless of how the character advances, this is not one of them. So I would change Giant's Might to be useable twice per short rest.
4) Runic Juggernaut seems a bit meh considering it is the capstone for the archetype. So I added that the duration of Giant's Might increases to 1 hour, and can be ended early by using a bonus action.