If your support staff isn't happy, you are doing something wrong
Helping others makes you happy. A number of studies have shown the positive impact of supporting others - not only on those who received the support but more markedly on those who offered help. Shouldn't that mean that people in support have a happiness advantage? Helping other people is part of the job description, after all.
There is one caveat though: research also shows negative consequences for givers who are overburdened or stressed by what they are doing, or who are giving so much they forget to take care of themselves. Helping others is great. Helping too much, or just pretending to help, however, has detrimental effects.
Your support people are the canaries in the coalmine!
They are probably stressed, but if on top of that you detect a lot of negative talk, unrest, and frustration, it's time to dig a bit deeper. What are the supporters pain points? Those are probably your customers' pain points too.
Too many people need help
If the number of requests you receive is too big to handle, you have several options:
You can hire more people.
You can give your team the resources to improve their answer rate - either by answering more requests or by shortening the number of interaction to resolution.
You can invest the time to analyze the type of requests and create resources that allow your customers to find the answers without a direct interaction.
If the surge in incoming requests is related to a one-time event (a product launch, a new feature, a marketing campaign), understanding the kind of questions that are being asked is super important: it is your path to further growth!
There is no help, only replies
Not being able to help is an extremely unpleasant experience (especially if you know you'll be subsequently rated based on the non-help you delivered). It happens though because a product is broken, promises weren't honored, or expectations weren't managed. These are your options:
Fix the product.
Be truthful when selling your product (looking at you, internet fiber company)
Listen to the needs of your customers - and help them finding an alternative if needed.
Don't expect your support people to calm your customers, if as a company you failed to deliver - customer support is not the last line of defense. It's the front line of excellence.