Changing the minimum TLS version of the Azure Storage account to TLS 1.2 should not impact your virtual machines or web applications as long as the operating systems, frameworks, and clients they use already support TLS 1.2, which is the case for all supported versions of Windows Server, IIS, .NET, and Microsoft SQL Server. TLS 1.2 has been the default and recommended secure protocol for several years, and modern Azure services and Microsoft platforms are designed to operate with it enabled.
Potential issues would only arise if there are legacy applications, outdated operating systems, old SQL Server versions, or custom integrations that are explicitly limited to TLS 1.0 or 1.1 when connecting to the storage account. In such cases, those components would need to be updated or reconfigured before enforcing TLS 1.2. This change does not affect internal VM operations by itself; it only affects how clients negotiate encryption when accessing the storage account endpoints.
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hth
Marcin