My main objective is to see where does my website ranks for a particular keyword in the SERP Results without any personalization effect.

What do you hope to achieve with this? I don't think that it is possible, but even if it is, no real human users would be searching for your website under those conditions. Your user's will all be subject to personalization, and thus see different SERP results. That is, different from non-personalized, and also different from each other. This is fundamentally the issue with the ranking tools, the tools have no way for accounting for this and thus the results from these tools cannot be trusted.

IMO the best tool you have Google Search Console, and it is far from being a great tool, the best of the worst.

What I want to do with this is that for example, I want to check my NEW client's website whether it is ranking for a particular keyword or not. And if it is ranking, then what page of the client's website is ranking with what rank on SERP?

This might give me the idea of whether it will be possible for me to rank on 1st page for that keyword using competitive analysis?

I hope my idea is clear?

I want to check my NEW client's website whether it is ranking for a particular keyword or not

What is the purpose of showing your client that his/her website ranks for a keyword, in conditions that will never be repeated in real life. The site could rank #1, but it will be of no value to your client because it will not generate any traffic.

If I were you I would go into GSC, go into the performance tab, select the keyword and print out the report. You need to pay particular attention to impressions, as this represents the number of times the website appears in search, this is the most important number. Then look at position, but note that position is the position given that there was an impression, not that there was a search made for that keyword. Example, all Google users search for widget 100 times in 30 days, your site has 50 impressions, and your position is 2. This means that the website appeared in 50% of the searches and when it appeared on average is appeared in the position 2. The big missing piece of information is that Google doesn't provide data on all the searches for a given keyword. The other issue with GSC and in particular with specific keywords is that here Google doesn't share all the keyword data and only provides keywords on something in the order of 10% of the searches. If you have a lot of traffic, that should be sufficient to provide a representative sample, but if traffic is low it can be very misleading. So you need to use the overall results (non-keyword specific) as a gauge.