Drupal - How to place Contact form in block?

Try Contact block module, which provides the contact form in a block.

From module documentation,

The Contact Block module provides contact forms in a block. It uses the contact forms that can be created using the Drupal 8 core Contact module.

Try https://www.drupal.org/project/entityform_block project, which allows you to create add form blocks for any entity type.

Create a new block type with an ER field that points to contact forms, enable contact_storage, and create a block, no coding required