Will my wife still be covered by Medicaid if I switch to Medicare?

Your Medicare is separate from hers. Call social security office and ask them. They have people who can explain your benefits and also explain how it will affect hers. You may also want to consult an estate planning attorney that specializes in estate planning for folks with public benefits specifically. There are ways to structure an estate plan, even one with ZERO real property, so that one's spend down is protected. Totally worth a free consult, especially if you own a home or think you may need long term care in the future.

You each receive Medicaid as individuals; that should stay the same, unless income increases. MediCare is not "income"; it is a medical coverage plan that accompanies SSI retirement.
If you were on SSDI/SSI for disability, prior to it converting to SSI Retirement, you might notice a bit of a decrease in the amount received, which is common when Disability converts to Retirement, for many recipients.
SSI disability is approximately similar to welfare, but recipients usually get more on that, than on straight welfare.
SSDI disability is for those who worked enough quarters, to qualify, so they get more than those on SSI Disability.
IF you were only receiving welfare, prior to starting your SSI retirement, your income might increase, and that might change your Welfare qualifications....unless you are still under-income with your Social Security.
One difference is, now you will also have MediCare [but your spouse won't, until she reaches retirement age].
MediCare reimburses better than Medicaid...so likely you get to choose from a few more Docs, than Medicaid patients...so your choices for care might increase a bit.
===IF you are under income, the normal, MediCare monthly premium that is deducted from the Social Security check/deposit, _can_ be paid for by a Federal program administered by State DSHS offices....so be sure to ask your Case Worker about that. That can free-up a bit over $100 per month that would normally be deducted.
===Talk with your Case Worker about your Social Security. They can tell you more exactly, what to expect from DSHS, now that your Social Security has begun.
ALSO:
All disabled persons on SSDI/SSI, and Maybe SSI Retirement, need to contact your legislators QUICK_ Tell them what you want them to do about the Social Security shortfall issue. They are debating how to handle the shortfalls in the funds.
Their solution so far most discussed, is to cut everyone's monthly checks by something like 19%, to keep funds coming longer than a year. The threat was, that if no cut is made, the funds will evaporate after about a year.
Some legislators propose to make even larger cuts.
I have not heard whether anyone suggests increasing payroll deductions [which would make more sense].
DSHS offices spent the last several years trying to move qualifying DSHS recipients over to Federal Disability coverage, to relieve State's budgets....now,
DSHS offices are on tenterhooks; they know that if big cuts in Social Security happen, loads of SSI/SSDI recipients will be back to seeking help from State DSHS, when States are mostly broke and cannot afford to fill in the gaps.
State DSHS statistics look good on paper, sort of, in that they can claim they are "helping notably more people"--unfortunately, they are helping them with far less amounts, and some services have been being cut.
A certain amount of this debacle, is related to some factions wanting desperately to Privatize Social Security.....that would be very bad....privatization has ruined every service it has gotten control of, for almost the past 100 years.
So please, contact your legislators, to tell them what you think they should do to solve this crisis, before it's too late! [if it's not already too late]

If your income doesn't change, she should still be eligible for Medicaid, but as the respondents above suggested, talk with your caseworker to be sure. You may also be eligible for Medicaid benefits to 'tie in' with medicare. Medicaid may cover your cost for Part B Medicare and act as a supplement to Medicare. It can be a big savings if you qualify for this benefit.

It is possible to be both on Medicare and Medicaid. Please talk to your caseworker about your change in status and income sources/amounts.

I would discuss it with your and your wife's Medicaid case worker. I don't know exactly how that works. I know that my cousin is on Medicare, due to being disabled. She received SS check and had Medicare medical coverage and then she really sick and got Medicaid coverage that steps in and pays what Medicare doesn't pay.