Ecom Labs - If you try and preview the page on a desktop, even in mobile view it does not display the correct blocks which is why it looks like that.
So the hamburger menu and the search block share a grid. The hamburger menu is set to display on mobile only.
I have managed to get the search bar onto the same line as the hamburger menu by assigning each block with display: inline-block; in css. I then simply set the search block to a width of 85% to ensure space on the line for the hamburger menu.
I have attached a screenshot of the results. I am pleased with this as when i asked CS-Cart direct i was told it would require paid modifications to achieve.
Perhaps you can also achieve this by changing your grid setting and adding a new grid parallel to search and adding humburger block into that grid. This way instead of looking on top of search your humburger layout looks in parallel and same will replicate on frontend too. https://prnt.sc/nma637
Please make sure that total sum of your grid division must be 16. See in my screenshot it is 3+3+10. Then in the grid of 10 if have to divide my blocks as per my choice like in 2,3,1 and so no but the total must be of 10. If you maintain this situation it will be in a row as you wanted.