Why is Payment Method "Manual" is not appearing in the Payment Form for Membership/Subscriptions?
If the Payment Method selected is "Manual" but in the related Payment Option has a picklist value of "One-Off-Authorise" in the "Frequency" field.
This will hide "Manual" Payment Method on the Payment Form as this frequency is NOT valid for Manual Payments and is reserved for Credit Cards and Direct Debits in some scenarios.
In order to show Manual on checkout form, you will have to make sure that frequency is NOT "One-Off-Authorise". This is particularly true if the related Payment Option is set as "Default"