It's hard to say.
Enough damage that it feels like performance has an impact on beating enrage timers or otherwise making the boss die faster. With enough scaling so that increasing gear within a tier feels like an improvement.
Ironically, the more "Tank Duties" that exist that pull away from focus on DPS, the more raw damage Tanks will require, so that when they've performed their duties well and get some time to drop some damage, that damage will feel like a meaningful contribution.
If you can think of a tank duty that doesn't result in a binary option, you're welcome to share it.
Personally, I once suggested a mechanic similar to XIII's Stagger system so Tanks could focus on creating burst windows against bosses which can scale infinitely with how fast they can create them and thus how many opportunities they can provide in a fight. Though, the downside is that it literally cannot function in XIV because this game is so heavily focused around everyone popping their 60/90/120s CD DPS cooldowns on 60/90/120 second intervals meaning that any burst window that doesn't line up with 60/90/120 second intervals is bad. (Also, they call this "Co-ordination" when people just press their CD's when they light upas opposed to other games where people actually co-ordinate because CD usage is determined via which boss phase to skip by bursting them down as well as a powerful once per fight Bloodlust/Heroism/Time Warp CD)
You mean the problem where the Dev's keep trying to find ways to artificially handicap Tank damage for... Reasons?
Being a useless meat shield is not appealing.
Trust me, I've played games where Tank damage was insignificant. Do you know what I did to optimize my gameplay? I pressed taunt then tabbed out to look at funny memes and only tabbed back in when boss was doing a tankbuster so I pressed a CD then went back to look at memes for the next minute.
Why? Because whether I was looking at funny memes or pressing attack buttons didn't affect the encounter at all, but one was infinitely more enjoyable (Hint: It was the memes)
One could argue that if mitigation was a more active part of combat theen being a useless meat shield would be more interesting and I wouldn't be able to tab out and look at funny memes. However, due to how binary tank duties are, you only need to actively mitigate enough to stay alive, which often isn't necessarily 100% engaging, especially once you gear up beyond minimum item levels (In addition to healers gearing up beyond minimum item levels, since that's the secondary factor in this, tanks required mitigation gets hit twice by gear increases because both your own mitigation and healer throughput increases)
Thus, once you hit the downtime between mitigating damage, which exponentially increases as your party gears up, you need something to do. Something that is engaging and feels worth your time to do. Thus, given limited options of things that are possible to do and feel worth your time, it comes down to damage, the ever present and infinitly scaling metric.
That's not the case.
Heck, I'm an active advocator of Tanks getting more Tank duties to perform, especially the removal of the horrible design which is passive defence that makes up 99% of your mitigation in favour of more engaging active defense skills (Which can be themed to each class, such as you can find in WoW. I.e. Warriors use Shield Block to guarantee blocked damage, Paladins use Shield of the Righteousness to increase their armour (Used to increase block chance), Death Knights use Death Strike to heal and create an absorb shield, Monks use Purifying Brew alongside passive delayed damage, Demon Hunters have Fel Spikes granting armour and parry and Druids have Ironfur increasing armour (Used to be Dodge which made little sense on the class that passively gains more max HP than other tanks))
It's just, being able to pack a punch alongside having tank duties is desired. Since, I've played enough games where the constant whining of DPS mains caused Tank damage to be neutered to the point where it just didn't feel good to play a Tank since all you really did was sit there like a target dummy and spam enmity/taunts.
Not to mention, the whole idea of "Why's the boss just attacking the one person who is not a threat?" being mitigated by you know, Tanks actually being a threat in their own right. Bosses should focus me because I'm kicking their ass.
In an ideal world, Tank damage and Tank duties would be intertwined. Meaning, a Tank performing a Tank duty of mitigating damage, is rewarded with damage. This damage, allows them to access another skill for mitigating damage to use against the next attack, thus gaining more damage.
With, again ideally, these damage increases being proportionate to how much you mitigate so that the better you mitigate damage the better your damage output and the better your damage output the better your mitigation options. (You know, as opposed to the old WoW Vengeance, which had reverse scaling because the attack power increase was based on damage taken after mitigation, meaning you ended up actively sabotaging your own mitigation to get more attack power...)