That will depend on your technical skills.  If you are comfortable to work inside the machine, there is no need for carry-in.  Customers install parts such as RAM, storage are not voiding warranty.  In fact, to assist you with the process, Dell provides the service manual with instructions for upgrading NVMe drive.  You can source the drive and work on it if you choose.

I suggest to have all your important data backup externally before working on the machine.  Following the safety precautions such as removing power source and wearing ESD wrist strap.

A new NVMe drive will certainly will speed up overall performance.  If you have had software issue(s), it may be better off to perform a clean install of OS.

Will my issue with windows be fixed if i were to add nvme2 ssd. Do i have to go the carry-in service center to do, this.
Dell ssd seems pricy in-comparison to Other popuplar brands. Even if i were to get the pricy dell ssd which have really low TBW, i would still lose my warranty because of the upgrade. So was wondering, what is the best option for me.

1. But the warranty i was provided with is no-upgrade warranty for 3 years. Currently 1.5 years have passed.

Am i not upgrading my device by adding ssd in m2 slot?

2. What will be my primary boot drive if i were to install ssd in m2 slot? Do i have change the settings in bios.

3. Is buying dell overpriced ssd even worth it?

1.  I could be wrong here but the term no-upgrade warranty was referring to the warranty policy itself, not about the computer products.  The warranty policy is different between regions, check for your actual service contracts.

2.  While many others would suggesting to clone your original drive to the new ssd when doing upgrade, I noted that your current hard drive is not performing well as standard.  Windows updates should not take over a day to complete or boot time of 30 minutes on a recent OptiPlex model is not acceptable.  Therefore, I suggested to do a fresh install on the new nvme ssd and it will be the main boot drive.  You can wipe the hard drive (delete all partitions) during Windows installation and use it for data drive.  Remember to review the installation process from the link provided earlier.  Check BIOS settings and enable AHCI for SATA operation mode. 

3.  It's a personal choice.  Dell brand for OptiPlex 5090 are just rebranded OEM from Samsung, Western Digital, Adata, Micron, and Kioxia.

https://www.dell.com/en-us/shop/dell-m2-pcie-nvme-gen-3x4-class-40-2280-solid-state-drive-512gb/apd/aa618641/storage-drives-media
This is dell version for ssd for my device i think.
I dont know the alternative in samsung.

Is it
a)980-pro-pcie-4-0-nvme-ssd-1tb-mz-v8p1t0b-am
b)980-pcie-3-0-nvme-gaming-ssd-1tb-mz-v8v1t0b-am

or something else. like evo plus 970?
Can you please suggest which to use that will work fine in optiplex 5090 sff
should i go for 512GB or 1TB or > 1TB

You mentioned. "I noted that your current hard drive is not performing well as standard. "
What do you mean, I checked with crystal disk info application and as well as speccy, both gave  me good for my hdd.
Should i get replacement with warranty?
Won't normal hdds, take have similar issues of 100% diskusage for 30 minutes during windows reboots?

When you check in Dell support website for OptiPlex 5090 storage drivers, you will find firmware updates for those ssd brands which commonly were shipped with OptiPlex 5090 systems.

Your selection of the gen4 Samsung 980 Pro 1tb looks good as it has both value and performance.  Although it won't be able to utilize full bandwidth, it's still an overall good choice. 

The gen 3 Samsung 980 is a budget item and while the performance is very good, it uses DRAM-less controller, so the write speed will slow down when running out of cache.

As for the original hard drive, based on the information you provided, system boot time was taken up to 30 min for the hard drive to slow down to idle state.  A heavy Windows updates would taken over a day to complete.  Those were not normal performances for hard drive.  But those issues were likely caused by software, not a hardware failure.  A SATA hard drive with Windows 10/11 system averagely takes 3 - 5 minutes to complete boot and less than an hour to complete multiple Windows updates.  Unless you get some kind of error code such as 2000-0142 at boot, you can't claim warranty.

Those were the reason why I was mentioning bad hard drive performances.  Also it was my reasoning for a fresh os install instead of cloning drive image to the new ssd 

Although it wasn't mentioned, you may consider to upgrade system ram (memory) as well.  Ideally, 16gb of ram is sufficient for normal usage, 64gb and up for heavy or professionals.

System boot time was taken up to 30 min for the hard drive to slow down to idle state (every reboot including update restarts ). Its not system boot time. I can log into windows as usual, but i can't open applications, since disk usage is 100%.
Ram max usage i have seen is around 8 GB. I don't think RAM is the issue.

If you have time, can you please tell me which is best option for my device. I don't know what to choose for ssd, whether it will be compatible or not. Are there any other versions out there compatible with  my device. or is my best option to buy dell version.?

Is crucial any good?
https://www.crucial.in/compatible-upgrade-for/dell/optiplex-5090-small-form-factor#ssd

If possible, can you list what all should i consider while making the purchase for best performance with my device.

Based on the site.
https://www.dell.com/support/manuals/en-in/optiplex-5090-desktop/d11_optiplex_5090_sff_ss/storage?guid=guid-3f3ccec0-9d0f-41a3-9451-e7b76ba12f65&lang=en-us

i only have gen3x4 not gen4x4 right?

After replacing the boot drive to an nvme ssd, you will see the different as day and night and all the issue with system slowness will be gone.

At this current time, the Samsung 980 Pro 1tb has the best value on their site and undisputedly best performance for your machine.  The pricing is also very competitive (69 usd).

The M.2 slot on your OptiPlex 5090 is gen3 x4, so a gen4 ssd will perform at gen3 speed, however, it will perform optimally while keeping the controller cool at the same time.  You may need to order an M2 screw, and there is no need to search further for ssd. 

Don't forget to take precaution steps while working on your components.