What a nice friend you are to ask about this.
This is all just my personal opinion, please someone else contradict me if necessary!
The new family will need time to settle in together as a family. You may need to wait to meet him, but be sure to say you do want to meet him at the right time, and if appropriate you and your friend could get together for some 'girl talk' when he is asleep before introducing your two little men! She may wish to chat about stuff without him around and just to relax and it may be helpful to do that if you and she wish, before the kids meet.
Your friend may well appreciate a cooked meal brought round just as other new mums do. We had this, and we have done this in our church and toddler group for new mums.
Your friend will almost certainly be advised that a soft play place may be over stimulating for a new child at first, too many people and too much going on! It may be easier at the right time to introduce your little boy to hers at a quieter spot, low key. Either his house or your house or somewhere very gentle like an out door place (weather permitting). Try not to add pressure by voicing to the children that they will be or become great friends, they may not like each other at first, but will probably become friends gradually.
You won't know about the child's previous family or life and your friend will hopefully have been advised that the story of this little boy's life is his story and not to be shared with anyone else. She may choose to explain some things he does or does not do or does or does not need, e.g. he may shout when worried, or go quiet when worried, he may need space, or he may need hugs etc. He may interrupt to get attention and whereas with a birth child you would say 'Wait, mummy is talking!' With a new child who has joined the family by adoption she may need to give him her full attention, as one might with a screaming new baby.
Good luck, I am sure you will be very supportive and your boys will learn to get along fine.
PS If you can please do give her a card to congratulate her on her son, maybe not a new baby card, but a special adoption one or a suitable blank card with simple wording and/or a simple gift for her (flowers) or for her son (a book) or whatever seems suitable. That is what happens when people have new babies and people who adopt will be just as likely to love some subtle TLC.