Two things: first of all, secure boot. Make sure it is disabled, since Ubuntu supports it, Manjaro does not.
Secondly, Ubuntu probably put itself on the fallback record of the ESP. You have two options - install 2 separate grubs and make sure they stay separate and are updated independently and select the desired OS from the UEFI menu, from time to time that might need reintalling grub, or use another Bootloader like Refind altogether.
In theory you can include Mangaro in the Ubuntu Grub und Ubuntu in the Manjaro grub, but that adds complexity and margin for errors and a lot of extra work, so i woul advise against.
If you decide to work with Grub(s) and switch always from the UEFI menu with F2 or F12 or whatever key is on your PC, you have to do the following reinstallation of grub 2 times:
Please read it, but it boils down to chrooting from USB live usb of manjaro and executing
grub-install --target=x86_64-efi --efi-directory=/boot/efi --bootloader-id=manjaro --recheck
Now you will have an entry manjaro in your EFI.
Then you do the same from ubuntu live iso (because grub version might be different). If you install ventoy on your usb stick you can just drop the 2 isos on it and avoid having 2 live usb
It will generally boil down to
sudo mount /dev/XXXXXXX /mnt
sudo mount /dev/YYYYYYYY /mnt/boot/efi
for dir in /dev /dev/pts /proc /sys /sys/firmware/efi/efivars /run; do sudo mount --bind $dir /mnt$dir; done
sudo chroot /mnt /bin/bash
grub-install --target=x86_64-efi --efi-directory=/boot/efi --bootloader-id=Ubuntu --recheck
Be very careful which partition is which…you can check from the liveusb with gparted for example, note the name of the manjaro, ubuntu (XXXXXX) und esp (YYYYYYY) partitions.
p.s. well, if chroot does not work we need to know why and you may need to chroot manually like in ubuntu which does not have such tool at all. Most probably you use BTRF filesystem, manjaro chroot does not work on that and you have to mount the volumes manually (there is a guide for mounting btrfs volumes and chrooting somewhere in the forum) but yourinxi -zv8 will tell us.
p.p.s. here it is, the btrfs mounting guide
Of course, the automatical chroot may just be confused by the 2 os-es and many partitions even of ext4. If in doubt do it manually as per the wiki