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I would store the bulbs for the winter.
Here is a link with storage information.

https://www.gardeningknowhow.com/ornamental/flowers/gladiola/storing-gladiola-corms.htm

This article will help you with winter storage for Gladiola corms.

https://www.gardeningknowhow.com/ornamental/bulbs/gladiola/storing-gladiola-corms.htm

There is little to be done if the corms have broke dormancy. Just allow them to grow and die off naturally.
It could effect the flowering the next season.

https://www.gardeningknowhow.com/ornamental/bulbs/gladiola/care-of-gladiolas-how-to-grow-gladiolas-in-your-garden.htm

You may be able to keep the sprouts from growing any more if you move the bulbs to a colder location. A refrigerator or cold garage could work, as described in this article:
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/how-to-store-bulbs-that-have-sprouted.htm

The bulbs will probably survive anyway; if anything some of them might not flower this year if they have used up too much energy in sprouting, but they might still be able to flower.

Unfortunately, digging your gladiolus up now will probably kill them, unless you plant them promptly in a new spot. Flowering uses up a lot of energy, and after flowering, the gladiolus use their leaves to store energy in the bulb for the following year, which is why it's best to wait until the leaves die back before digging them up for storage. It might be possible to dig them up in late summer or so, but that might inhibit them from flowering the following year.

Yes, the bulbs can be saved. In your warm region, the bulbs can be left in the ground although gladiolus experts often choose to lift their bulbs at the end of the season.

Allow the plants to stay in the garden until the foliage yellows. During this period the bulbs are gathering strength for next year's show. Then lift, trim and store in a dry, non-freezing location.

See tips here:https://www.leafari.com/gladiolus-planting-guide.html