I can't specify the type of fungus, but you have a succulent there in a very wet conditions. Succulents prefer a very dry arid condition with minimal water. Think Xeriscape.

I agree this isn't a fungus. it looks like one of the stonecrop type succulents.

Agree one of the stonecrops

If you mean the white bumps, some of those might be root nodes, but why is this piece sitting in water? If you're trying to root it this way, and the white bumps are fluffy (its impossible to tell even under magnification), which would indicate mould, its because its in water, or has been kept in very wet conditions. The piece of plant does resemble a stonecrop of some sort, but its hard to be 100% without seeing the rest of the plant - is it outdoor or indoor?

I don't know what kind of succulent it is, but the white stuff is some kind of scale insect, not a fungus. Many insecticides are effective on scale, especially when mixed with a surfactant. Organically, kill the juveniles by spraying with soapy water, then go to work on the adults. Break as many off manually as you can without stripping the leaves, and then go after the hiders with a small paint brush dipped in rubbing alcohol (meths). It may take several weeks of work to get all of them, and you may need to spray again to catch a second hatch of juveniles. Spray neem oil on nearby plants to keep them from catching them.

I think the white bumps may be mealy bugs. Try squashing one and see if its red inside. If that's what they are painting them with meths will kill them immediately.
The eggs are like white cotton wool and meths will kill those as well as the mature insects. If the roots are infected too you can in fact clean them as well if you dip them in a shallow container of it and make sure every bit of root comes into contact with it.
Cacti and succulents are particularly prone to attack, especially if they get very pot bound. If the white patches are also on the inside of the pot wipe that over with meths as well. Once the plant is clean you can pot it up it in dry open gritty compost and don't water at all for several weeks and then only sparingly.

To be on the safe side you can take a cutting, but not the way you just did - succulents are different. Take your cutting and leave it for a few hours for the cut surface to dry. Then insert it in open dry gritty compost (you can buy special cactus compost if you are unsure)and don't water it at all until it has rooted well. One light watering a month is all most succulents need in winter, and even in summer once a week to once a fortnight is plenty, depending on how hot it is. Succulents are designed to live in dry warm places with little rainfall. When they are really thirsty they will lose their shine.

Sorry Tug, you beat me to it.

'Sallright! :)

This looks like a Jade Plant. They are very resilient & that piece should root readily if you put it in a cactus mix.

'Keep soil moist but not wet during active growth in the spring and summer. Allow soil to dry between waterings in the winter. Avoid splashing water on the leaves while watering.'

https://www.almanac.com/plant/jade-plant