Manage Permissions of List Item as "Normal" User

ftfaul here below you can find a possible approach

Important Note: SharePoint OOTB is not designed to provide this flexibility in terms of Group permission at item level. Please do a very extensive test phase to avoid security breaches.

The View/Edit part

1. Create 3 SharePoint Groups:
   Group A,Group B,Group C
2. Create a Custom Column in your list. Something like "VisibleToGroup" (Type: Person/Groups - ChooseFrom: All Users)
3. Create a Custom View "Filtered Results" (Add A filter - CreatedBy [Me]) -- You will set later this view as default -- As filter you can put whatever you want. The idea is to have a <Where> section to the web part's XML already populated
4. Use SharePoint Designer to edit the View you have created above and replace the <Where> code with the following

  <Where>
    <Membership Type="CurrentUserGroups">
      <FieldRef Name="VisibleToGroup"/>
    </Membership>
  </Where>

The Permissions part

1. Create a MSFT Form or Nintex Form that allow Users to request access to Group A,B,C
2. Link a Power Automate flow that will be triggered after the Form submission
3. Create a Power Automate that perform a REST API call to add the user to the Group

Last Note: The Automation part does not include a rollback scenario. You have to set up a proper Governance to ensure users are removed from Group A,B,C when their job is done (maybe an additional Power Automate that runs every end of the months and reset the permissions to initial state)