Two PHP core on one hosting

I have one hosting, in root FTP one.

I created a new folder in the root of /project
In the root .htaccess I edited the file like this

<IfModule mod_rewrite.c>
    RewriteEngine on

    RewriteCond %{HTTP_HOST} ^project\.domain\.com$
    RewriteCond %{REQUEST_URI} !^/project/
    RewriteCond %{DOCUMENT_ROOT}/project -d
    RewriteRule ^(.*)$ /project/$1 [L]

    RewriteRule    ^(\.well-known/.*)$ $1 [L]
    RewriteRule    ^$    webroot/    [L]
    RewriteRule    (.*) webroot/$1    [L]
</IfModule>

If I call project.domain.com, the page is loaded, but if the link is in the page, it adds /project/url before the URL … how to set PHP Cake so that the folder name is not added to the URL?

It should behave as if I have a website in the root hosting.

Thank You

I created .htaccess on root server:

RewriteEngine On

RewriteCond %{HTTP_HOST} ^one\.phpcake$ [NC]
RewriteRule ^(.*)$ /one/$1 [L]

RewriteCond %{HTTP_HOST} ^two\.phpcake$ [NC]
RewriteRule ^(.*)$ /two/$1 [L]

Its works, but if request authorization, then redirect eg. url is:

https://one.phpcake/one/login

This url works: https://one.phpcake/login but if in the page link to other, this href is https://one.phpcake/one/password

How to solve it so that it doesn’t put /one/ there?