Can I use Terminal emulator on the Web Browser in Ubuntu?

You can use node environment for it.

Then install web-terminal

npm install web-terminal -g
web-terminal --port 8088

just open that link in your browser:

http://localhost:8088/terminal/

You can add a new entry to startup applications to launch it automatically at startup.

gnome-session-properties

Open that window, name your entry and add the command in it or add the path of your bash script.

EDIT:

There are many alternatives, one of them I used in the past wetty You can search for them in github and nmp

EDIT2:

It's not a good idea to use a terminal emulator on your web browser. If you don't feel secure in your local network and you are not behind a firewall router, attackers may infiltrate in your operating system.

EDIT3:

Closing the assigned port to incoming connection attempts via ufw blocks accession to your computer from local network or internet.

 sudo ufw enable
 sudo ufw deny in 8088

Check out the status of your firewall:

 sudo ufw status

I suggest using an ssh client in the browser. Either as a browser extension e.g. Secure Shell App, or an ssh client written in javascript.

There are other good posts in this topic: Is there a web based terminal/ssh client?