[Hydrogen Skeleton] Issues with Predictive Search + Search page improvements

[BrendaSegalShopify]

What is the location of your example repository?

Hydrogen Skeleton

Which package or tool is having this issue?

Hydrogen

What version of that package or tool are you using?

xxxxx

What version of Remix are you using?

No response

Steps to Reproduce

cc @juanpprieto this is the issue covering what we discussed in our Hydrogen Developer Tools research meeting.

Predictive Search

1. When typing in a letter, the Predictive Search results show, but then are immediately reloaded with the empty state
2. The search button doesn't work

Storefront Search

For the Storefront Search results, we should add:

1. trackingParameters (these are included in Predictive Search results already, I believe)
2. Images
3. Pricing (for products)

Expected Behavior

Already described in the steps to reproduce

Actual Behavior

Already described in the steps to reproduce

[vitaliy-bobrov]

I believe the problem with predictive search was caused by enabling 'v3_fetcherPersist' flag in config, with this one set to false it works as expected.