This video explains how to check if current user belongs to SharePoint Group On App Start and Set the Startscreen based on membership.

Video also explains OnStart and StartScreen Property and their usage and workaround.
Below are formulas used:
PowerAutomate
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api call
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_api/web/sitegroups/getByName(‘Finance Group’)/Users?filter=Email eq ‘@{triggerBody()[‘text’]}’

compose
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body(‘Send_an_HTTP_request_to_SharePoint’)[‘d’][‘results’]

condition equals
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equals(String(outputs(‘Compose’)),'[]’)

PowerApps
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OnStart
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Set(isMember,CheckFinanceGroupMembership.Run(User().Email).ismember);
If(isMember = “True”, Set(navigationTarget, “Scr_Search”), Set(navigationTarget, “Scr_NoAccess”))

Timer controls
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AutStart :true

OnTimerEnd
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If(navigationTarget = “Scr_Search”, Navigate(Scr_Search),Navigate(Scr_NoAccess));