WP installed on a sub domain and wanting to use URL FWD

i have got our WP installed on a sub domain, eg.. https://www.example.com/wordpress

we have a new domain name registered eg. https://www.new-wp-site.com and we have directed it to https://www.example.com/wordpress
Wth URL masking on, so it does not change from https://www.new-wp-site.com

Whilst it is working great. I have noticed any home page or logo within my WP page is linked to the original https://www.example.com/wordpress

which does not matter because my https://www.new-wp-site.com has URL masking active.

But its an issue when User right click and select OPEN in NEW Window… then of cos, it will open as https://www.example.com/wordpress

I have tried to change in settings> general
WordPress Address (URL) and Site Address (URL)

but cannot get it to do what I want, which is to have all home page links and home logos in WP to link to https://www.new-wp-site.com which will load WP off the sub domain..etc… just a forwarding Loop as to say…

Is this even possible ? or am I barking up the wrong tree?

Any advice is much appreciated.

thanks!