I have this exact same problem: https://projectdmc.org/support/topic/plugin-not-working-with-cf7/
If I enable CF integration on this plugin settings, no form will work, with or without the [cf7-simple-turnstile] shortcode.
For example, here: https://ptwooplugins.com/pre-sales-questions/
The shortcode is there:
<label> Name
[text* your-name autocomplete:name] </label><label> Email
[email* your-email autocomplete:email] </label>
<label> Subject
[text* your-subject] </label>
<label> Plugin
[select plugin "- Not related to a plugin -" "DPD Pickup and Lockers for WooCommerce" "DPD Portugal for WooCommerce" "Feed KuantoKusta for WooCommerce" "InvoiceXpress for WooCommerce" "Multibanco, … (IfthenPay) for WooCommerce" "Multicaixa (ProxyPay) for WooCommerce" "Portuguese Postcodes for WooCommerce" "Shop as Client for WooCommerce" "Simple Custom Fields for WooCommerce Blocks Checkout" "Simple WooCommerce Order Approval" "Taxonomy Discounts for WooCommerce" "Other (specify in message)"] </label>
<label> Your message (optional)
[textarea your-message] </label>
[cf7-simple-turnstile][submit "Send"]