Usually, the smoke of a volcano – and in particular the sulphur dioxide contained inside the smoke cloud – ultimately leads to a cooling of Earth's surface for a short period.
This is because the sulphur dioxide transforms into sulphate aerosols, which send sunlight back into space before it reaches the surface. This shading effect means the surface cools down for a while, until the sulphate falls back down to the surface or gets rained out.
This is not what happened for Hunga Tonga.
Because it was an underwater volcano, Hunga Tonga produced little smoke, but a lot of water vapor: 100–150 million tonnes, or the equivalent of 60,000 Olympic swimming pools. The enormous heat of the eruption transformed huge amounts of sea water into steam, which then shot high into the atmosphere with the force of the eruption.
All that water ended up in the stratosphere: a layer of the atmosphere between about 15 and 40 kilometers above the surface, which produces neither clouds nor rain because it is too dry.
Water vapour in the stratosphere has two main effects. One, it helps in the chemical reactions which destroy the ozone layer, and two, it is a very potent greenhouse gas.
There is no precedent in our observations of volcanic eruptions to know what all that water would do to our climate, and for how long. This is because the only way to measure water vapour in the entire stratosphere is via satellites. These only exist since 1979, and there hasn't been an eruption similar to Hunga Tonga in that time.
