Sorry if the formatting is a little rough, I'm writing this on mobile.

Short answer: Actual numbers on growth are hard to come by, but population growth for jellyfish species is expected to continue, though I personally doubt they'll ever completely take over fish in the near future.

Long Answer: When you hear about Jellyfish populations exploding, generally people are referring to Jellyfish blooms. This is a completely natural phenomenon which occurs when the polyp (the benthic attached asexual form) develops into the medusa, which is the freefloating sexual organism most people know as jellyfish. This makes jellyfish populations look like they've exploded out of nowhere and is when people start to get concerned. It's also where a lot of population studies take place (except for one which focuses on the polyps, I'll link further reading below.) They also follow a "boom-and-bust" model, where essentially all the jellyfish within the bloom with die at once. While the blooms are natural, that doesn't mean they're without consequence, and areas with unnaturally large blooms can be negatively affected by them.

All of that being said, it's really hard to get an accurate measure on population data for jellyfish. This is a modern problem without much baseline data, and is sadly common in wildlife studies as people tended not to really care much in the past about things that become problems in the future. So instead of trying to track growth, scientists focus on the factors which cause blooms and try to create models for the future to predict how, when, and what size they will occur at.

With all the preamble out of the way, All the sources I've read point at 2 main environmental factors which influence jellyfish blooms.

(1) Temperature. Higher temperatures create larger blooms

(2) Fish Population. Areas with a depleted fish stock from fishing are more likely to have more and larger blooms

With current climate trends, global ocean temperatures have been steadily rising. This has undoubtedly been contributing to larger and more frequent blooms. Additionally, this has other effects such as increasing microforage which jellyfish rely on further increasing their growth. Fish populations are also expected to decline both due to unsustainable fishing operations and climate change, leading to a potential increase of jellyfish.

So while there has been an increase in the number and intensity of blooms, we dont have much in the way of tracking blooms historically. But we have a pretty good idea of how events may unfold in the future.

Additional reading

A Modeling Study on Population Dynamics of Jellyfish Aurelia aurita in the Bohai and Yellow Seas

Population dynamics, growth and predation impact of the common jellyfish Aurelia aurita and two hydromedusae, Sarsia tubulosa, and Aequorea vitrina in Limfjorden (Denmark)

Modeling population dynamics of scyphozoan jellyfish (Aurelia spp.) in the Gulf of Mexico

Jellyfish and ctenophore blooms coincide with human proliferations and environmental perturbation

Ecological drivers of jellyfish blooms – The complex life history of a ‘well-known’ medusa (Aurelia aurita)