Train transfer at Birmingham

Look at schedules at https://www.westmidlandsrailway.co.uk/
There's two stations you could depart from -- Worcester Foregate St and Worcester Shub Hill.

There are trains departing each hour at :47 direct from Worcester Shrub Hill to Stratford-upon-Avon with a 1:56 journey time. If you depart from Worcester Foregate St, those journeys tend to include the change from Birmingham New Street to Birmingham Moor St. I've never done that transfer but it's 0.3 of a mile walk.

If you don't want to make the walking connection between New Street & Moor Street there is an hourly West Midlands train that goes direct via Moor Street only. It is a local service that stops a lot more on the way so finishes up only marginally quicker (bit over 2 hours) but may suit your needs better.

It isn't a solid 25 minutes walk between the 2 Birmingham stations though for most people as this is a conservative specified connection time. Nearly all can be done undercover via interlinked shopping centre in bad weather (there is an outside street route as well).

It is nothing like a 25 minute walk. The distance is under 400 yards, and is signposted. It is just straight along a street.

In the opposite direction Moor Street to New Street you turn left out of the station entrance, almost immediately cross the street at a light controlled crossing then bear slightly right with the road on a wide sidewalk through a tunnel under the shopping centre. As you come out of the tunnel there is an entrance to the shopping centre on your left and you will see the piazza to the New Street Station entrance on your right. Cross the street to the entrance on a light controlled pedestrian crossing here.

It almost takes longer to write the above than to do the walk.

The slightly longer route is to bear a bit left down the hill at the 1st set of lights, then walk through the shopping centre- you are far more likely to get lost or diverted on that route (and end up having spent money!).

Towards Moor Street New Street station has multiple exits - all clearly signed. Find the right exit then just reverse the directions.

EDIT- I do the New Street to Moor Street transfer on auto pilot, so was having problems describing the right New Street exit to you- but here is a PDF plan of New Street for you- https://www.networkrail.co.uk/wp-content/uploads/2022/03/Birmingham-New-Street-Station-Map.pdf
I know it says 600 metres, the sign at Moor Street says 280 metres (!!), which I think is far more correct.

The key is to find the huge mechanical metal bull marked on the map (Ozzy the Bull). Find that (and you can't possibly miss him) and you can't go wrong.

The 25 minute time allowance comes by adding up the following 3 parts:

Birmingham New Street: Minimum interchange time 12 minutes
Walking time between New Street and Moor Street 8 minutes
Birmingham Moor Street: Minimum interchange time 5 minutes

This as I said earlier is by intention conservative but maybe more so than usual by adding up the three separate bits but are also based on people having no prior knowledge of the station(s) and the location.

I've always prefered to go up to the shopping malls and walk through that way, eventually taking the escalators all the way down to the ground floor at Moor Street. I enjoy the many food outlets and window shopping as I walk through - sometimes it is fast, sometimes slower because of distractions. Be sure which platform you need at Moor Street, there is a lift and a bridge, but if you stay outside the station and walk just past the entrance there is another way down to the usual platform to Stratford-upon-Avon.

But, maybe the very best is just to settle into the through train from Worcester if you don't mind missing the bit of exercise or lunch stop half way through. Horses for courses whatever you prefer. There are two trains to Stratford every hour, at xx:55 and xx:39, you can take any of them unless you are on a restricted "Advance" ticket.