Unfortunately right now Animate isn't able to export animated SVG files.
You can try some extensions but I'm not sure if there is one that actually works these days.
Please request this feature to the Animate team if you wish:
I believe you can open the SVG in adobe illustrator and copy what you want out of illustrator and paste it right into adobe animate.
So there is actually an extension that will export animated SVGs but it's not really updated/supported much and is VERY finicky.
BUT it DOES work! Just make sure of a few things...
1. unlock ALL layers before exporting (including nested layers)
2. Try to have all animation on main timeline
3. If step 2 isn't possible, make sure nested timlines are as long as the main timeline
4. Don't use grouped assets, use Object Drawing assets or select them, and go to Modify > Combine Objects > Union
5. You may have to convert all tweens to keyframed animations - especially if easing is applied.
It took me a lot of trial and error to get past the hurdles and jump through the hoops to get it to work successfully but when it does, it's a LIFESAVER! I just wish AnCC had Animated SVG as a document type natively!