[3.x]: Extend ElementQuery and being unable to modify the list of sites using siteId()

What happened?

Description

I've created a Widget that makes a query and wanted to filter by site, but I always get the default site in the query instead

        $submissions = Submission::find()
            ->siteId($this->sites) // this does nothing
            ->siteIdOverride($this->sites) // this sets the siteId correct site list 
            ->all();

class SubmissionQuery extends ElementQuery
{
    /**
     * Can't use siteId directly, since it will be overwritten when the prepare method is called
     *
     * @param array $value
     * @return $this
     */
    public function siteIdOverride(array $value): self
    {
        $this->sitesOverride = $value;
        return $this;
    }

    protected function beforePrepare(): bool
    {
        $sites = $this->siteId; // has default site in it
        $sitesOverride = $this->sitesOverride; // correct list of sites

        $this->siteId($this->sitesOverride);

        return parent::beforePrepare();
    }
}

Expected behavior

If a site is already set, craft should perform the query with that siteId instead

Actual behavior

$siteId will be overwriten with the default site in the prepare statement

Craft CMS version

3.7.26

PHP version

8.1

Operating system and version

No response

Database type and version

No response

Image driver and version

No response

Installed plugins and versions

Start with the SubmissionQuery example and trace ElementQuery's beforePrepare handling of siteId, including when the default site is applied. Reproduce the query using an explicitly supplied site list and confirm that the generated query uses that list instead of overwriting it with the default site.