RF2 settings on the Sky box only affect the aerial pass-thru picture, not the HDMI or the SCART socket.
Your picture shrunk a little with the TV menu picture setting on Custom because Overscan was disabled in that mode. Overscan is a legacy setting from the days of CRT TVs. It predates 16:9. Depending on the preset built in to your TV, Overscan On/Off will change the picture size equally in height and width by 2-4%.
Where you're watching a HD channel from Sky - say BBC 1 HD or BBC News HD - they've got pretty good standards, and so people should look the correct shape, not short and squashed vertically. Flick over to ch 588 EWTN Catholic and you should see what poor standards look like. On the section I have just found, the picture should be 4:3 because it's obviously stretch out horizontally to fill a 16:9 screen. Second, with Overscan swiched off, I can see some dashes at the top edge of the screen. This should really be out of the frame as it's above what's known as the active picture area. They've also screwed up the aspect ratio flagging because my TV doesn't switch to 4:3 mode when set to Auto.
Question 1: Do you have the Sky box connected via HDMI directly to the TV, or is the picture going through some other device such as an AV Receiver or soundbar?
Question 2: Is your new TV substantially bigger in screen size that the previous sets?