Stamina doesn’t regenerate while blocking. You Cant Regen Stamina While Blocking.
When you are blocking, you do not regenerate Stamina. If I spend some Stamina and hold block, my Stamina bar doesn’t move as when I am blocking my Stamina recovery is turned off. This is one of the root causes for a lot of beginner Tank deaths is permanently blocking then running out of Stamina, each time an enemy hits you, you lose the value of Stamina in relation to whatever your Block Cost is. You will still regenerate Magicka in this situation which makes Magicka Recovery and Magicka resources important as a Tank. As soon as you drop your block your Stamina will regenerate. If you have less Stamina than your “Block Cost” then you will automatically drop block and you are unable to re-block until you have enough Stamina to do so.
You can gain Stamina back while blocking via other sources aside from Stamina regeneration such as Potions, Absorb Stamina enchants on your 1 handed weapon, and utilising Skills and Passives that give back resources such as using a Magicka costing Draconic Power skill on a DK (Igneous Shield), Bull Netch on Warden, Leeching Strikes on a NB, Restoring Focus on a Templar. Sorcerers have Dark Deal but that forces you to drop block for a very short time as you cast it. You can also follow the “Heavy after a Heavy” trick which is where you Heavy Attack the enemy immediately after they Heavy Attack you as this is the main window of opportunity to do so in almost every single PvE combat situation.
You can block with Magicka. If you take the Destruction Staff passive “Tri-Focus” this will cause the opposite effect where you block with Magicka and you cannot regenerate Magicka but you will regenerate Stamina. Personally I do not use this and never intend to do so outside of 1 or 2 very precise situations because almost all Tank skills are Magicka costing, if you then lose Magicka constantly from your Block Cost along with a Max Magicka of 20-25k you soon start to run out and this also means you cannot heal since your main Tank heals and shield are usually Magicka costing also.
In a lot of situations you may only be using Stamina to block and Pierce Armor and nothing else, maybe the occasionally Roll Dodge or Break Free so you have way less resource drain by Blocking using Stamina and prioritising the use of Magicka skills.
You can potentially use blocking with both resources as a method of safety as you can bar swap and block with alternative resources but its generally not worth it since you’ll have low Stamina Recovery and recovery ticks every 2 seconds so it would just be faster to Heavy Attack or use a Magicka Costing skill to give you back Stamina.
For more help – check out the Beginner Tank Guide and The Tank Club Discord.