First, you'll need to make sure that your new AdSense account is fully approved and active. You can do this by checking your AdSense account status in the "Earnings" tab. Once your new account is active, you can then replace the AdSense code on your website with the new code from the new account.
You should also be aware that replacing the AdSense ID on your website may affect your existing ads and earnings, as your new ads may not be targeted to your audience as well as your previous ads were. However, you should also see improvements in your earnings over time as you optimize your ads.
Regarding setting your new Google account with blogger account, you need to go to blogger.com and sign in with your new google account, then navigate to "settings" and select "permissions" and add your new google account as an admin.
Please be aware that you should read the Adsense policies and guidelines before replacing your publisher ID to avoid any issues.
I find that the harder I work, the more luck I seem to have.