How do I play a support barb on season 21?

Support barbarians are only more defensive than an offensive barbarian because of their choice of stats on gear and passives, the actual legendary items they pick do not tend directly make them more defensive with the exception of their weapons (as opposed to a support Monk which tends to take abilities and items that give damage reduction and healing). This means you can expect to take more damage than your damage-focused ally if they have much better gear than you and you're playing at their difficulty level. If you do not have both Little Rogue and The Slanderer, your best bet is to use your best rolled weapon and shield. Stormshield is suggested because it has a higher base block chance than other shields, but any shield is generally better than a weapon for this. The Raekor's set does not have a damage reduction with 4 pieces like other sets, its main survivability is in constantly moving with Furious Charge and the Cold Rush rune you get for free when using it. The way you stay alive is by constantly charging so that enemies miss you with abilities combined with the frozen effect from that rune, to keep this up you need to take advantage of the refund effect from the Raekor's 2-set ability and the CDR from Merciless Charge rune - long story short, try to always hit at least one enemy when using charge, and if you have to hit more than one try to hit as many as possible. You can also switch Oculus Ring to Band of Might for extra damage reduction if you still find you can't survive at the rift level your allies play at.

Your job in the dungeon is to buff your group and debuff enemies near them, then run ahead to try to drag more enemies toward the group and scout the dungeon. You should only be near other group members long enough to refresh their Ignore Pain and re-apply debuffs to enemies. In a Greater Rift there are generally enough grouped enemies that you should be able to get most of your Furious Charge back when you use it, which you should take advantage of to find the correct path forward in the dungeon and any elite packs off the main path. In a 2's group you may need to spend more time grouping enemies for your ally if they can't do it themselves, try to experiment with how and when you can leave them to get more enemies and scout and see what works best for you. With 3 or 4 people you'll likely have at least one ally that can handle grouping the mobs once they get to your allies and you can focus on scouting.

There's another variant of the support build to play that Icy-Veins hasn't listed, which is to effectively switch the Raekor's set pieces with Wrath of the Wastes instead and use Whirlwind instead of Furious Charge. If you have The Slanderer and Little Rogue you can keep those, but if not you should also look for the Bul-Kathos Mighty Weapon set for this build. Its main advantage over the Raekor's build is that it adds 50% passive damage reduction when using Whirlwind, so while it isn't quite as mobile everything will do less damage. You can take a look through the group leaderboards to see how people are doing this.