Multi-select isn't combining without a reload

If selecting several tags still navigates to a new page, rather than updating instantly, this is almost always expected behaviour for your specific theme rather than a fault.

Check whether your theme supports it at all

Instant, no-reload multi-select needs the filter to be placed inside your blog section as an app block, support that themes built on Shopify's Horizon foundation have and Dawn's blog template does not. See Theme compatibility for the full comparison, and Add the filter to your theme for how the block was actually placed on your store.

If the block was added as its own separate section, the option that works on every theme, normal page navigation on each tag change is the correct, expected fallback, not a malfunction. Multi-select still works in every case; it just isn't instant.

Confirm the feature is actually turned on

Multi-select is available on any paid plan, turned on from the Design page's Behaviour section. If it's off, tags behave as single-select links regardless of theme.

Still combining tags, but always reloading, even on a supporting theme

If your theme is one that should support the instant behaviour and it's still always reloading, contact support and include your shop domain, theme name, and the blog's URL.