After transfer wordpress to different hosting, they have different preview

What’s the site address? Static pictures like these are not helpful in troubleshooting design/layout issues.

The browser for the most part determine how the page looks. Did you adjust any settings or blocks after moving. Also, if you made changes on any of the pages and didn’t export them and you did not copy your database over, You would lose those changes. All your changes live inside your database not in the physical files in the directory. They are only sent to the physical file if you do an export. After making changes to pages it would probably be a good ideal to export theme. The theme.json file also can effects how the site looks and behaves. The Theme.json is used to tweak the layout of the site. It can control what fonts are being used it can also create styles for your blocks and sections and for your layout. It also can allow you to change the appearance of individual blocks, or prevent users from changing styles and limit color pallets, or override and disable default pallets. Changes to any or all of this files could and probably would effect the appearance of your site.

It looks like the css for the navigation block is not correct in the new site. Some of the rules seem to be missing. The rules are part of the nav block configuration. Example this rule should be present

@media (min-width: 600px)
.wp-block-navigation__responsive-container-open:not(.always-shown) {
    display: none;
}

It toggles the hamburger menu on and off but it doesn’t appear in the css of your new site. Not sure why it not there. It seems the problem is with the styling of the nav block on your site. The X is for a dialog block not sure what triggering it. It has a class of

wp-block-navigation__responsive-dialog

couldn’t find the rule for it. It could be triggered by javascript but there no error in the console. But, It doesn’t appear that the blocks are being configured right. You could try updating wordpress to see if it fixes the problem. The styles for the blocks are contained in the react block files.

It appears to me that the problem is with reading the style sheets that are stored in the blocks. You might want to reach out to your host provider to see if there some kind of authority issue. Here a thread of a similar issue. You might find something in it that will help. https://wordpress.org/support/topic/core-block-stylesheets-not-loading/