The only way to Get the list of Files available in Azure Repo is Rest API call. For this we have to use the PowerShell.
Used to retrieve the Repos
GET https://dev.azure.com/{organization}/{project}/_apis/git/repositories?api-version=5.1
# With Optional Parameter
GET https://dev.azure.com/{organization}/{project}/_apis/git/repositories?includeLinks={includeLinks}&includeAllUrls={includeAllUrls}&includeHidden={includeHidden}&api-version=5.1
It Get the content of Single item. Download parameter is used to check whether we can download the content or not.
GET https://dev.azure.com/{organization}/{project}/_apis/git/repositories/{repositoryId}/items?path={path}&api-version=5.1
# With Optional Parameter
GET https://dev.azure.com/{organization}/{project}/_apis/git/repositories/{repositoryId}/items?path={path}&scopePath={scopePath}&recursionLevel={recursionLevel}&includeContentMetadata={includeContentMetadata}&latestProcessedChange={latestProcessedChange}&download={download}&$format={$format}&versionDescriptor.versionOptions={versionDescriptor.versionOptions}&versionDescriptor.version={versionDescriptor.version}&versionDescriptor.versionType={versionDescriptor.versionType}&includeContent={includeContent}&resolveLfs={resolveLfs}&api-version=5.1
You can implement above Api in your PowerShell accordingly. Refer here for how to implement this in PowerShell.