1) Your existing web.config: you have declared rewrite map .. but have not created any rules that will use it. RewriteMap on its' own does absolutely nothing.
2) Below is how you can do it (it does not utilise rewrite maps -- rules only, which is fine for small amount of rewrites/redirects):
This rule will do SINGLE EXACT rewrite (internal redirect) /page to /page.html. URL in browser will remain unchanged.
<system.webServer>
<rewrite>
<rules>
<rule name="SpecificRewrite" stopProcessing="true">
<match url="^page$" />
<action type="Rewrite" url="/page.html" />
</rule>
</rules>
</rewrite>
</system.webServer>
This rule #2 will do the same as above, but will do 301 redirect (Permanent Redirect) where URL will change in browser.
<system.webServer>
<rewrite>
<rules>
<rule name="SpecificRedirect" stopProcessing="true">
<match url="^page$" />
<action type="Redirect" url="/page.html" />
</rule>
</rules>
</rewrite>
</system.webServer>
Rule #3 will attempt to execute such rewrite for ANY URL if there are such file with .html extension (i.e. for /page it will check if /page.html exists, and if it does then rewrite occurs):
<system.webServer>
<rewrite>
<rules>
<rule name="DynamicRewrite" stopProcessing="true">
<match url="(.*)" />
<conditions>
<add input="{REQUEST_FILENAME}\.html" matchType="IsFile" />
</conditions>
<action type="Rewrite" url="/{R:1}.html" />
</rule>
</rules>
</rewrite>
</system.webServer>